We develop a framework for the average-case analysis of random quadratic problems and derive algorithms that are optimal under this analysis. This yields a new class of methods that achieve acceleration given a model of the Hessian's eigenvalue distribution. We develop explicit algorithms for the uniform, Marchenko-Pastur, and exponential distributions. These methods are momentum-based algorithms, whose hyper-parameters can be estimated without knowledge of the Hessian's smallest singular value, in contrast with classical accelerated methods like Nesterov acceleration and Polyak momentum. Through empirical benchmarks on quadratic and logistic regression problems, we identify regimes in which the the proposed methods improve over classical (worst-case) accelerated methods.

Node classification in attributed graphs is an important task in multiple practical settings, but it can often be difficult or expensive to obtain labels. Active learning can improve the achieved classification performance for a given budget on the number of queried labels. The best existing methods are based on graph neural networks, but they often perform poorly unless a sizeable validation set of labelled nodes is available in order to choose good hyperparameters. We propose a novel graph-based active learning algorithm for the task of node classification in attributed graphs; our algorithm uses graph cognizant logistic regression, equivalent to a linearized graph-convolutional neural network (GCN), for the prediction phase and maximizes the expected error reduction in the query phase. To reduce the delay experienced by a labeller interacting with the system, we derive a preemptive querying system that calculates a new query during the labelling process, and to address the setting where learning starts with almost no labelled data, we also develop a hybrid algorithm that performs adaptive model averaging of label propagation and linearized GCN inference. We conduct experiments on five public benchmark datasets, demonstrating a significant improvement over state-of-the-art approaches and illustrate the practical value of the method by applying it to a private microwave link network dataset.

Adversarial Multi-task Representation Learning (AMTRL) methods are able to boost the performance of Multi-task Representation Learning (MTRL) models. However, the theoretical mechanism behind AMTRL is less investigated. To fill this gap, we study the generalization error bound of AMTRL through the lens of Lagrangian duality . Based on the duality, we proposed an novel adaptive AMTRL algorithm which improves the performance of original AMTRL methods. The extensive experiments back up our theoretical analysis and validate the superiority of our proposed algorithm.

The empirical performance of neural ordinary differential equations (NODEs) is significantly inferior to discrete-layer models on benchmark tasks (e.g. image classification). We demonstrate an explanation is the inaccuracy of existing gradient estimation methods: the adjoint method has numerical errors in reverse-mode integration; the naive method suffers from a redundantly deep computation graph. We propose the Adaptive Checkpoint Adjoint (ACA) method: ACA applies a trajectory checkpoint strategy which records the forward- mode trajectory as the reverse-mode trajectory to guarantee accuracy; ACA deletes redundant components for shallow computation graphs; and ACA supports adaptive solvers. On image classification tasks, compared with the adjoint and naive method, ACA achieves half the error rate in half the training time; NODE trained with ACA outperforms ResNet in both accuracy and test-retest reliability. On time-series modeling, ACA outperforms competing methods. Furthermore, NODE with ACA can incorporate physical knowledge to achieve better accuracy.

Optimizing the parameters of partial differential equations (PDEs), i.e., PDE-constrained optimization (PDE-CO), allows us to model natural systems from observations or perform rational design of structures with complicated mechanical, thermal, or electromagnetic properties. However, PDE-CO is often computationally prohibitive due to the need to solve the PDE---typically via finite element analysis (FEA)---at each step of the optimization procedure. In this paper we propose amortized finite element analysis (AmorFEA), in which a neural network learns to produce accurate PDE solutions, while preserving many of the advantages of traditional finite element methods. This network is trained to directly minimize the potential energy from which the PDE and finite element method are derived, avoiding the need to generate costly supervised training data by solving PDEs with traditional FEA. As FEA is a variational procedure, AmorFEA is a direct analogue to popular amortized inference approaches in latent variable models, with the finite element basis acting as the variational family. AmorFEA can perform PDE-CO without the need to repeatedly solve the associated PDE, accelerating optimization when compared to a traditional workflow using FEA and the adjoint method.

This paper studies a problem of learning surface mesh via implicit functions in an emerging field of deep learning surface reconstruction, where implicit functions are popularly implemented as multi-layer perceptrons (MLPs) with rectified linear units (ReLU). To achieve meshing from the learned implicit functions, existing methods adopt the de-facto standard algorithm of marching cubes; while promising, they suffer from loss of precision learned in the MLPs, due to the discretization nature of marching cubes. Motivated by the knowledge that a ReLU based MLP partitions its input space into a number of linear regions, we identify from these regions analytic cells and faces that are associated with zero-level isosurface of the implicit function, and characterize the conditions under which the identified faces are guaranteed to connect and form a closed, piecewise planar surface. We propose a naturally parallelizable algorithm of analytic marching to exactly recover the mesh captured by a learned MLP. Experiments on deep learning mesh reconstruction verify the advantages of our algorithm over existing ones.

The use of machine learning algorithms in finance, medicine, and criminal justice can deeply impact human lives. As a consequence, research into interpretable machine learning has rapidly grown in an attempt to better control and fix possible sources of mistakes and biases. Tree ensembles, in particular, offer a good prediction quality in various domains, but the concurrent use of multiple trees reduces the interpretability of the ensemble. Against this background, we study born-again tree ensembles, i.e., the process of constructing a single decision tree of minimum size that reproduces the exact same behavior as a given tree ensemble in its entire feature space. To find such a tree, we develop a dynamic-programming based algorithm that exploits sophisticated pruning and bounding rules to reduce the number of recursive calls. This algorithm generates optimal born-again trees for many datasets of practical interest, leading to classifiers which are typically simpler and more interpretable without any other form of compromise.

Lying at the core of human intelligence, relational thinking is characterized by initially relying on innumerable unconscious percepts pertaining to relations between new sensory signals and prior knowledge, consequently becoming a recognizable concept or object through coupling and transformation of these percepts. Such mental processes are difficult to model in real-world problems such as in conversational automatic speech recognition (ASR), as the percepts (if they are modelled as graphs indicating relationships among utterances) are supposed to be innumerable and not directly observable. In this paper, we present a Bayesian nonparametric deep learning method called deep graph random process (DGP) that can generate an infinite number of probabilistic graphs representing percepts. We further provide a closed-form solution for coupling and transformation of these percept graphs for acoustic modeling. Our approach is able to successfully infer relations among utterances without using any relational data during training. Experimental evaluations on ASR tasks including CHiME-2 and CHiME-5 demonstrate the effectiveness and benefits of our method.

Embedding layers are commonly used to map discrete symbols into continuous embedding vectors that reflect their semantic meanings. Despite their effectiveness, the number of parameters in an embedding layer increases linearly with the number of symbols and poses a critical challenge on memory and storage constraints. In this work, we propose a generic and end-to-end learnable compression framework termed differentiable product quantization (DPQ). We present two instantiations of DPQ that leverage different approximation techniques to enable differentiability in end-to-end learning. Our method can readily serve as a drop-in alternative for any existing embedding layer. Empirically, DPQ offers significant compression ratios (14-238X) at negligible or no performance cost on 10 datasets across three different language tasks.

Generative adversarial networks (GANs) represent a zero-sum game between two machine players, a generator and a discriminator, designed to learn the distribution of data. While GANs have achieved state-of-the-art performance in several benchmark learning tasks, GAN minimax optimization still poses great theoretical and empirical challenges. GANs trained using first-order optimization methods commonly fail to converge to a stable solution where the players cannot improve their objective, i.e., the Nash equilibrium of the underlying game. Such issues raise the question of the existence of Nash equilibria in GAN zero-sum games. In this work, we show through theoretical and numerical results that indeed GAN zero-sum games may have no Nash equilibria. To characterize an equilibrium notion applicable to GANs, we consider the equilibrium of a new zero-sum game with an objective function given by a proximal operator applied to the original objective, a solution we call the proximal equilibrium. Unlike the Nash equilibrium, the proximal equilibrium captures the sequential nature of GANs, in which the generator moves first followed by the discriminator. We prove that the optimal generative model in Wasserstein GAN problems provides a proximal equilibrium. Inspired by these results, we propose a new approach, which we call proximal training, for solving GAN problems. We perform several numerical experiments indicating the existence of proximal equilibria in GANs.

One of the most surprising and exciting discoveries in supervised learning was the benefit of overparameterization (i.e. training a very large model) to improving the optimization landscape of a problem, with minimal effect on statistical performance (i.e. generalization). In contrast, unsupervised settings have been under-explored, despite the fact that it was observed that overparameterization can be helpful as early as Dasgupta & Schulman (2007). We perform an empirical study of different aspects of overparameterization in unsupervised learning of latent variable models via synthetic and semi-synthetic experiments. We discuss benefits to different metrics of success (recovering the parameters of the ground-truth model, held-out log-likelihood), sensitivity to variations of the training algorithm, and behavior as the amount of overparameterization increases. We find that across a variety of models (noisy-OR networks, sparse coding, probabilistic context-free grammars) and training algorithms (variational inference, alternating minimization, expectation-maximization), overparameterization can significantly increase the number of ground truth latent variables recovered.

There has been recent interest in improving performance of simple models for multiple reasons such as interpretability, robust learning from small data, deployment in memory constrained settings as well as environmental considerations. In this paper, we propose a novel method SRatio that can utilize information from high performing complex models (viz. deep neural networks, boosted trees, random forests) to reweight a training dataset for a potentially low performing simple model of much lower complexity such as a decision tree or a shallow network enhancing its performance. Our method also leverages the per sample hardness estimate of the simple model which is not the case with the prior works which primarily consider the complex model's confidences/predictions and is thus conceptually novel. Moreover, we generalize and formalize the concept of attaching probes to intermediate layers of a neural network to other commonly used classifiers and incorporate this into our method. The benefit of these contributions is witnessed in the experiments where on 6 UCI datasets and CIFAR-10 we outperform competitors in a majority (16 out of 27) of the cases and tie for best performance in the remaining cases. In fact, in a couple of cases, we even approach the complex model's performance. We also conduct further experiments to validate assertions and intuitively understand why our method works. Theoretically, we motivate our approach by showing that the weighted loss minimized by simple models using our weighting upper bounds the loss of the complex model.

To collect large scale annotated data, it is inevitable to introduce label noise, i.e., incorrect class labels. To be robust against label noise, many successful methods rely on the noisy classifiers (i.e., models trained on the noisy training data) to determine whether a label is trustworthy. However, it remains unknown why this heuristic works well in practice. In this paper, we provide the first theoretical explanation for these methods. We prove that the prediction of a noisy classifier can indeed be a good indicator of whether the label of a training data is clean. Based on the theoretical result, we propose a novel algorithm that corrects the labels based on the noisy classifier prediction. The corrected labels are consistent with the true Bayesian optimal classifier with high probability. We incorporate our label correction algorithm into the training of deep neural networks and train models that achieve superior testing performance on multiple public datasets.

Group fairness, a class of fairness notions that measure how different groups of individuals are treated differently according to their protected attributes, has been shown to conflict with one another, often with a necessary cost in loss of model's predictive performance. We propose a general diagnostic that enables systematic characterization of these trade-offs in group fairness. We observe that the majority of group fairness notions can be expressed via the fairness-confusion tensor, which is the confusion matrix split according to the protected attribute values. We frame several optimization problems that directly optimize both accuracy and fairness objectives over the elements of this tensor, which yield a general perspective for understanding multiple trade-offs including group fairness incompatibilities. It also suggests an alternate post-processing method for designing fair classifiers. On synthetic and real datasets, we demonstrate the use cases of our diagnostic, particularly on understanding the trade-off landscape between accuracy and fairness.

Trustworthy AI is a critical issue in machine learning where, in addition to training a model that is accurate, one must consider both fair and robust training in the presence of data bias and poisoning. However, the existing model fairness techniques mistakenly view poisoned data as an additional bias to be fixed, resulting in severe performance degradation. To address this problem, we propose FR-Train, which holistically performs fair and robust model training. We provide a mutual information-based interpretation of an existing adversarial training-based fairness-only method, and apply this idea to architect an additional discriminator that can identify poisoned data using a clean validation set and reduce its influence. In our experiments, FR-Train shows almost no decrease in fairness and accuracy in the presence of data poisoning by both mitigating the bias and defending against poisoning. We also demonstrate how to construct clean validation sets using crowdsourcing, and release new benchmark datasets.

Deep-learning-based methods for various applications have been shown vulnerable to adversarial examples. Here we address the use of deep-learning networks as inverse problem solvers, which has generated much excitement and even adoption efforts by the main equipment vendors for medical imaging including computed tomography (CT) and MRI. However, the recent demonstration that such networks suffer from a similar vulnerability to adversarial attacks potentially undermines their future. We propose to modify the training strategy of end-to-end deep-learning-based inverse problem solvers to improve robustness. To this end, we introduce an auxiliary net-work to generate adversarial examples, which is used in a min-max formulation to build robust image reconstruction networks. Theoretically, we argue that for such inverse problem solvers, one should analyze and study the effect of adversaries in the measurement-space, instead of in the signal-space used in previous work. We show for a linear reconstruction scheme that our min-max formulation results in a singular-value filter regularized solution, which suppresses the effect of adversarial examples. Numerical experiments using the proposed min-max scheme confirm convergence to this solution. We complement the theory by experiments on non-linear Compressive Sensing(CS) reconstruction by a deep neural network on two standard datasets, and, using anonymized clinical data, on a state-of-the-art published algorithm for low-dose x-ray CT reconstruction. We show a significant improvement in robustness over other methods for deep network-based reconstruction, by using the proposed approach.

The Transformer architecture has achieved considerable success recently; the key component of the Transformer is the attention layer that enables the model to focus on important regions within an input sequence. Gradient optimization with attention layers can be notoriously difficult requiring tricks such as learning rate warmup to prevent divergence. As Transformer models are becoming larger and more expensive to train, recent research has focused on understanding and improving optimization in these architectures. In this work our contributions are two-fold: we first investigate and empirically validate the source of optimization problems in the encoder-decoder Transformer architecture; we then propose a new weight initialization scheme with theoretical justification, that enables training without warmup or layer normalization. Empirical results on public machine translation benchmarks show that our approach achieves leading accuracy, allowing to train deep Transformer models with 200 layers in both encoder and decoder (over 1000 attention/MLP blocks) without difficulty. Code for this work is available here:~\url{https://github.com/layer6ai-labs/T-Fixup}.

Studying the set of exact solutions of a system of polynomial equations largely depends on a single iterative algorithm, known as Buchberger’s algorithm. Optimized versions of this algorithm are crucial for many computer algebra systems (e.g., Mathematica, Maple, Sage). We introduce a new approach to Buchberger’s algorithm that uses reinforcement learning agents to perform S-pair selection, a key step in the algorithm. We then study how the difficulty of the problem depends on the choices of domain and distribution of polynomials, about which little is known. Finally, we train a policy model using proximal policy optimization (PPO) to learn S-pair selection strategies for random systems of binomial equations. In certain domains, the trained model outperforms state-of-the-art selection heuristics in total number of polynomial additions performed, which provides a proof-of-concept that recent developments in machine learning have the potential to improve performance of algorithms in symbolic computation.

We study problems where a learner aims to learn the valuations of an agent by observing which goods he buys under varying price vectors. More specifically, we consider the case of a $k$-demand agent, whose valuation over the goods is additive when receiving up to $k$ goods, but who has no interest in receiving more than $k$ goods. We settle the query complexity for the active-learning (preference elicitation) version, where the learner chooses the prices to post, by giving a {\em biased binary search} algorithm, generalizing the classical binary search procedure. We complement our query complexity upper bounds by lower bounds that match up to lower-order terms. We also study the passive-learning version in which the learner does not control the prices, and instead they are sampled from some distribution. We show that in the PAC model for passive learning, any {\em empirical risk minimizer} has a sample complexity that is optimal up to a factor of $\widetilde{O}(k)$.

Linear constrained convex programming (LCCP) has many practical applications, including support vector machine (SVM) and machine learning portfolio (MLP) problems. We propose the randomized primal-dual coordinate (RPDC) method, a randomized coordinate extension of the first-order primal-dual method by Cohen and Zhu, 1984 and Zhao and Zhu, 2019, to solve LCCP. We randomly choose a block of variables based on the uniform distribution and apply linearization and a Bregman-like function (core function) to the selected block to obtain simple parallel primal-dual decomposition for LCCP. We establish almost surely convergence and expected O(1/t) convergence rate. Under global strong metric subregularity, we establish the linear convergence of RPDC. Finally, we discuss the implementation details of RPDC and present numerical experiments on SVM and MLP problems to verify the linear convergence.

We present three new algorithms for constructing differentially private synthetic data---a sanitized version of a sensitive dataset that approximately preserves the answers to a large collection of statistical queries. All three algorithms are \emph{oracle-efficient} in the sense that they are computationally efficient when given access to an optimization oracle. Such an oracle can be implemented using many existing (non-private) optimization tools such as sophisticated integer program solvers. While the accuracy of the synthetic data is contingent on the oracle's optimization performance, the algorithms satisfy differential privacy even in the worst case. For all three algorithms, we provide theoretical guarantees for both accuracy and privacy. Through empirical evaluation, we demonstrate that our methods scale well with both the dimensionality of the data and the number of queries. Compared to the state-of-the-art method High-Dimensional Matrix Mechanism (McKenna et al.~VLDB 2018), our algorithms provide better accuracy in the large workload and high privacy regime (corresponding to low privacy loss $\eps$).

In this work, we propose a robust test for the multivariate two-sample problem through projective ensemble, which is a generalization of the Cramer-von Mises statistic. The proposed test statistic has a simple closed-form expression without any tuning parameters involved, it is easy to implement can be computed in quadratic time. Moreover, our test is insensitive to the dimension and consistent against all fixed alternatives, it does not require the moment assumption and is robust to the presence of outliers. We study the asymptotic behaviors of the test statistic under the null and two kinds of alternative hypotheses. We also suggest a permutation procedure to approximate critical values and employ its consistency. We demonstrate the effectiveness of our test through extensive simulation studies and a real data application.

Local graph clustering and the closely related seed set expansion problem are primitives on graphs that are central to a wide range of analytic and learning tasks such as local clustering, community detection, semi-supervised learning, nodes ranking and feature inference. Prior work on local graph clustering mostly falls into two categories with numerical and combinatorial roots respectively, in this work we draw inspiration from both fields and propose a family of convex optimization formulations based on the idea of diffusion with $p$-norm network flow for $p\in (1,\infty)$. In the context of local clustering, we characterize the optimal solutions for these optimization problems and show their usefulness in finding low conductance cuts around input seed set. In particular, we achieve quadratic approximation of conductance in the case of $p=2$ similar to the Cheeger-type bounds of spectral methods, constant factor approximation when $p\rightarrow\infty$ similar to max-flow based methods, and a smooth transition for general $p$ values in between. Thus, our optimization formulation can be viewed as bridging the numerical and combinatorial approaches, and we can achieve the best of both worlds in terms of speed and noise robustness. We show that the proposed problem can be solved in strongly local running time for $p\ge 2$ and conduct empirical evaluations on both synthetic and real-world graphs to illustrate our approach compares favorably with existing methods.

The change-point detection problem seeks to identify distributional changes in streams of data. Increasingly, tools for change-point detection are applied in settings where data may be highly sensitive and formal privacy guarantees are required, such as identifying disease outbreaks based on hospital records, or IoT devices detecting activity within a home. Differential privacy has emerged as a powerful technique for enabling data analysis while preventing information leakage about individuals. Much of the prior work on change-point detection---including the only private algorithms for this problem---requires complete knowledge of the pre-change and post-change distributions, which is an unrealistic assumption for many practical applications of interest. This work develops differentially private algorithms for solving the change-point detection problem when the data distributions are unknown. Additionally, the data may be sampled from distributions that change smoothly over time, rather than fixed pre-change and post-change distributions. We apply our algorithms to detect changes in the linear trends of such data streams. Finally, we also provide experimental results to empirically validate the performance of our algorithms.

Temporal difference (TD) learning is one of the main foundations of modern reinforcement learning. This paper studies the use of TD(0), a canonical TD algorithm, to estimate the value function of a given policy from a batch of data. In this batch setting, we show that TD(0) may converge to an inaccurate value function because the update following an action is weighted according to the number of times that action occurred in the batch -- not the true probability of the action under the given policy. To address this limitation, we introduce \textit{policy sampling error corrected}-TD(0) (PSEC-TD(0)). PSEC-TD(0) first estimates the empirical distribution of actions in each state in the batch and then uses importance sampling to correct for the mismatch between the empirical weighting and the correct weighting for updates following each action. We refine the concept of a certainty-equivalence estimate and argue that PSEC-TD(0) is a more data efficient estimator than TD(0) for a fixed batch of data. Finally, we conduct an empirical evaluation of PSEC-TD(0) on three batch value function learning tasks, with a hyperparameter sensitivity analysis, and show that PSEC-TD(0) produces value function estimates with lower mean squared error than TD(0).

Motivated by the repeated sale of online ads via auctions, optimal pricing in repeated auctions has attracted a large body of research. While dynamic mechanisms offer powerful techniques to improve on both revenue and efficiency by optimizing auctions across different items, their reliance on exact distributional information of buyers' valuations (present and future) limits their use in practice. In this paper, we propose robust dynamic mechanism design. We develop a new framework to design dynamic mechanisms that are robust to both estimation errors in value distributions and strategic behavior. We apply the framework in learning environments, leading to the first policy that achieves provably low regret against the optimal dynamic mechanism in contextual auctions, where the dynamic benchmark has full and accurate distributional information.

Adversarial robustness has become a fundamental requirement in modern machine learning applications. Yet, there has been surprisingly little statistical understanding so far. In this paper, we provide the first result of the \emph{optimal} minimax guarantees for the excess risk for adversarially robust classification, under Gaussian mixture model proposed by \cite{schmidt2018adversarially}. The results are stated in terms of the \emph{Adversarial Signal-to-Noise Ratio (AdvSNR)}, which generalizes a similar notion for standard linear classification to the adversarial setting. For the Gaussian mixtures with AdvSNR value of $r$, we prove an excess risk lower bound of order $\Theta(e^{-(\frac{1}{2}+o(1)) r^2} \frac{d}{n})$ and design a computationally efficient estimator that achieves this optimal rate. Our results built upon minimal assumptions while cover a wide spectrum of adversarial perturbations including $\ell_p$ balls for any $p \ge 1$.

Computational equilibrium finding in large zero-sum extensive-form imperfect-information games has led to significant recent AI breakthroughs. The fastest algorithms for the problem are new forms of counterfactual regret minimization (Brown & Sandholm, 2019). In this paper we present a totally different approach to the problem, which is competitive and often orders of magnitude better than the prior state of the art. The equilibrium-finding problem can be formulated as a linear program (LP) (Koller et al., 1994), but solving it as an LP has not been scalable due to the memory requirements of LP solvers, which can often be quadratically worse than CFR-based algorithms. We give an efficient practical algorithm that factors a large payoff matrix into a product of two matrices that are typically dramatically sparser. This allows us to express the equilibrium-finding problem as a linear program with size only a logarithmic factor worse than CFR, and thus allows linear program solvers to run on such games. With experiments on poker endgames, we demonstrate in practice, for the first time, that modern linear program solvers are competitive against even game-specific modern variants of CFR in solving large extensive-form games, and can be used to compute exact solutions unlike iterative algorithms like CFR.

We present a new class of stochastic, geometrically-driven optimization algorithms on the orthogonal group O(d) and naturally reductive homogeneous manifolds obtained from the action of the rotation group SO(d). We theoretically and experimentally demonstrate that our methods can be applied in various fields of machine learning including deep, convolutional and recurrent neural networks, reinforcement learning, normalizing flows and metric learning. We show an intriguing connection between efficient stochastic optimization on the orthogonal group and graph theory (e.g. matching problem, partition functions over graphs, graph-coloring). We leverage the theory of Lie groups and provide theoretical results for the designed class of algorithms. We demonstrate broad applicability of our methods by showing strong performance on the seemingly unrelated tasks of learning world models to obtain stable policies for the most difficult Humanoid agent from OpenAI Gym and improving convolutional neural networks.

Beyond machine learning's success in the specific tasks, research for learning multiple tasks simultaneously is referred to as multi-task learning. However, existing multi-task learning needs manual definition of tasks and manual task annotation. A crucial problem for advanced intelligence is how to understand the human task concept using basic input-output pairs. Without task definition, samples from multiple tasks are mixed together and result in a confusing mapping challenge. We propose Confusing Supervised Learning (CSL) that takes these confusing samples and extracts task concepts by differentiating between these samples. We theoretically proved the feasibility of the CSL framework and designed an iterative algorithm to distinguish between tasks. The experiments demonstrate that our CSL methods could achieve a human-like task understanding without task labeling in multi-function regression problems and multi-task recognition problems.

Network quantization is essential for deploying deep models to IoT devices due to its high efficiency. Most existing quantization approaches rely on the full training datasets and the time-consuming fine-tuning to retain accuracy. Post-training quantization does not have these problems, however, it has mainly been shown effective for 8-bit quantization due to the simple optimization strategy. In this paper, we propose a Bit-Split and Stitching framework (Bit-split) for lower-bit post-training quantization with minimal accuracy degradation. The proposed framework is validated on a variety of computer vision tasks, including image classification, object detection, instance segmentation, with various network architectures. Specifically, Bit-split can achieve near-original model performance even when quantizing FP32 models to INT3 without fine-tuning.

Polyak momentum (PM), also known as the heavy-ball method, is a widely used optimization method that enjoys an asymptotic optimal worst-case complexity on quadratic objectives. However, its remarkable empirical success is not fully explained by this optimality, as the worst-case analysis --contrary to the average-case-- is not representative of the expected complexity of an algorithm. In this work we establish a novel link between PM and the average-case analysis. Our main contribution is to prove that \emph{any} optimal average-case method converges in the number of iterations to PM, under mild assumptions. This brings a new perspective on this classical method, showing that PM is asymptotically both worst-case and average-case optimal.

Meta-learning algorithms produce feature extractors which achieve state-of-the-art performance on few-shot classification. While the literature is rich with meta-learning methods, little is known about why the resulting feature extractors perform so well. We develop a better understanding of the underlying mechanics of meta-learning and the difference between models trained using meta-learning and models which are trained classically. In doing so, we introduce and verify several hypotheses for why meta-learned models perform better. Furthermore, we develop a regularizer which boosts the performance of standard training routines for few-shot classification. In many cases, our routine outperforms meta-learning while simultaneously running an order of magnitude faster.

We present a new active learning algorithm that adaptively partitions the input space into a finite number of regions, and subsequently seeks a distinct predictor for each region, while actively requesting labels. We prove theoretical guarantees for both the generalization error and the label complexity of our algorithm, and analyze the number of regions defined by the algorithm under some mild assumptions. We also report the results of an extensive suite of experiments on several real-world datasets demonstrating substantial empirical benefits over existing single-region and non-adaptive region-based active learning baselines.

Graphical modeling has been broadly useful for exploring the dependence structure among features in a dataset. However, the strength of graphical modeling hinges on our ability to encode and estimate conditional dependencies. In particular, commonly used measures such as partial correlation are only meaningful under strongly parametric (in this case, multivariate Gaussian) assumptions. These assumptions are unverifiable, and there is often little reason to believe they hold in practice. In this paper, we instead consider 3 non-parametric measures of conditional dependence. These measures are meaningful without structural assumptions on the multivariate distribution of the data. In addition, we show that for 2 of these measures there are simple, strong plug-in estimators that require only the estimation of a conditional mean. These plug-in estimators (1) are asymptotically linear and non-parametrically efficient, (2) allow incorporation of flexible machine learning techniques for conditional mean estimation, and (3) enable the construction of valid Wald-type confidence intervals. In addition, by leveraging the influence function of these estimators, one can obtain intervals with simultaneous coverage guarantees for all pairs of features.

In recent years, a variety of gradient-based bi-level optimization methods have been developed for learning tasks. However, theoretical guarantees of these existing approaches often heavily rely on the simplification that for each fixed upper-level variable, the lower-level solution must be a singleton (a.k.a., Lower-Level Singleton, LLS). In this work, by formulating bi-level models from the optimistic viewpoint and aggregating hierarchical objective information, we establish Bi-level Descent Aggregation (BDA), a flexible and modularized algorithmic framework for bi-level programming. Theoretically, we derive a new methodology to prove the convergence of BDA without the LLS condition. Furthermore, we improve the convergence properties of conventional first-order bi-level schemes (under the LLS simplification) based on our proof recipe. Extensive experiments justify our theoretical results and demonstrate the superiority of the proposed BDA for different tasks, including hyper-parameter optimization and meta learning.

The variance reduction class of algorithms including the representative ones, SVRG and SARAH, have well documented merits for empirical risk minimization problems. However, they require grid search to tune parameters (step size and the number of iterations per inner loop) for optimal performance. This work introduces almost tune-free' SVRG and SARAH schemes equipped with i) Barzilai-Borwein (BB) step sizes; ii) averaging; and, iii) the inner loop length adjusted to the BB step sizes. In particular, SVRG, SARAH, and their BB variants are first reexamined through anestimate sequence' lens to enable new averaging methods that tighten their convergence rates theoretically, and improve their performance empirically when the step size or the inner loop length is chosen large. Then a simple yet effective means to adjust the number of iterations per inner loop is developed to enhance the merits of the proposed averaging schemes and BB step sizes. Numerical tests corroborate the proposed methods.

Clustering is a foundational problem in machine learning with numerous applications. As machine learning increases in ubiquity as a backend for automated systems, concerns about fairness arise. Much of the current literature on fairness deals with discrimination against protected classes in supervised learning (group fairness). We define a different notion of fair clustering wherein the probability that two points (or a community of points) become separated is bounded by an increasing function of their pairwise distance (or community diameter). We capture the situation where data points represent people who gain some benefit from being clustered together. Unfairness arises when certain points are deterministically separated, either arbitrarily or by someone who intends to harm them as in the case of gerrymandering election districts. In response, we formally define two new types of fairness in the clustering setting, pairwise fairness and community preservation. To explore the practicality of our fairness goals, we devise an approach for extending existing $k$-center algorithms to satisfy these fairness constraints. Analysis of this approach proves that reasonable approximations can be achieved while maintaining fairness. In experiments, we compare the effectiveness of our approach to classical $k$-center algorithms/heuristics and explore the tradeoff between optimal clustering and fairness.

We study the bandit problem where the underlying expected reward is a Bounded Mean Oscillation (BMO) function. BMO functions are allowed to be discontinuous and unbounded, and are useful in modeling signals with singularities in the domain. We develop a toolset for BMO bandits, and provide an algorithm that can achieve poly-log $\delta$-regret -- a regret measured against an arm that is optimal after removing a $\delta$-sized portion of the arm space.

Finite-horizon sequential experimental design (SED) arises naturally in many contexts, including hyperparameter tuning in machine learning among more traditional settings. Computing the optimal policy for such problems requires solving Bellman equations, which are generally intractable. Most existing work resorts to severely myopic approximations by limiting the decision horizon to only a single time-step, which can underweight exploration in favor of exploitation. We present BINOCULARS: Batch-Informed NOnmyopic Choices, Using Long-horizons for Adaptive, Rapid SED, a general framework for deriving efficient, nonmyopic approximations to the optimal experimental policy. Our key idea is simple and surprisingly effective: we first compute a one-step optimal batch of experiments, then select a single point from this batch to evaluate. We realize BINOCULARS for Bayesian optimization and Bayesian quadrature -- two notable example problems with radically different objectives -- and demonstrate that BINOCULARS significantly outperforms significantly outperforms myopic alternatives in real-world scenarios.

In many practical applications, heuristic or approximation algorithms are used to efficiently solve the task at hand. However their solutions frequently do not satisfy natural monotonicity properties expected to hold in the optimum. In this work we develop algorithms that are able to restore monotonicity in the parameters of interest. Specifically, given oracle access to a possibly non monotone function, we provide an algorithm that restores monotonicity while degrading the expected value of the function by at most $\epsilon$. The number of queries required is at most logarithmic in $1/\epsilon$ and exponential in the number of parameters. We also give a lower bound showing that this exponential dependence is necessary. Finally, we obtain improved query complexity bounds for restoring the weaker property of $k$-marginal monotonicity. Under this property, every $k$-dimensional projection of the function is required to be monotone. The query complexity we obtain only scales exponentially with $k$ and is polynomial in the number of parameters.

Variational inference (VI) and Markov chain Monte Carlo (MCMC) are approximate posterior inference algorithms that are often said to have complementary strengths, with VI being fast but biased and MCMC being slower but asymptotically unbiased. In this paper, we analyze gradient-based MCMC and VI procedures and find theoretical and empirical evidence that these procedures are not as different as one might think. In particular, a close examination of the Fokker-Planck equation that governs the Langevin dynamics (LD) MCMC procedure reveals that LD implicitly follows a gradient flow that corresponds to an VI procedure based on optimizing a nonparametric normalizing flow. The evolution under gradient descent of real-world VI approximations that use tractable, parametric flows can thus be seen as an approximation to the evolution of a population of LD-MCMC chains. This result suggests that the transient bias of LD (due to the Markov chain not having burned in) may track that of VI (due to the optimizer not having converged), up to differences due to VI’s asymptotic bias and parameter geometry. Empirically, we find that the transient biases of these algorithms (and their momentum-accelerated counterparts) do evolve similarly. This suggests that practitioners with a limited time budget may get more accurate results by running an MCMC procedure (even if it is stopped before fully burning in) than a VI procedure, as long as the variance of the MCMC estimator can be dealt with (e.g., by running many parallel chains).

Generative adversarial networks (GANs) variants approximately minimize divergences between the model and the data distribution using a discriminator. Wasserstein GANs (WGANs) enjoy superior empirical performance, however, unlike in f-GANs, the discriminator does not provide an estimate for the ratio between model and data densities, which is useful in applications such as inverse reinforcement learning. To overcome this limitation, we propose an new training objective where we additionally optimize over a set of importance weights over the generated samples. By suitably constraining the feasible set of importance weights, we obtain a family of objectives which includes and generalizes the original f-GAN and WGAN objectives. We show that a natural extension outperforms WGANs while providing density ratios as in f-GAN, and demonstrate empirical success on distribution modeling, density ratio estimation and image generation.

Building accurate language models that capture meaningful long-term dependencies is a core challenge in natural language processing. Towards this end, we present a calibration-based approach to measure long-term discrepancies between a generative sequence model and the true distribution, and use these discrepancies to improve the model. Empirically, we show that state-of-the-art language models, including LSTMs and Transformers, are miscalibrated: the entropy rates of their generations drift dramatically upward over time. We then provide provable methods to mitigate this phenomenon. Furthermore, we show how this calibration-based approach can also be used to measure the amount of memory that language models use for prediction.

Latent confounders---unobserved variables that influence both treatment and outcome---can bias estimates of causal effects. In some cases, these confounders are shared across observations, e.g. all students in a school are influenced by the school's culture in addition to any educational interventions they receive individually. This paper shows how to model latent confounders that have this structure and thereby improve estimates of causal effects. The key innovations are a hierarchical Bayesian model, Gaussian processes with structured latent confounders (GP-SLC), and a Monte Carlo inference algorithm for this model based on elliptical slice sampling. GP-SLC provides principled Bayesian uncertainty estimates of individual treatment effect with minimal assumptions about the functional forms relating confounders, covariates, treatment, and outcomes. This paper also proves that, for linear functional forms, accounting for the structure in latent confounders is sufficient for asymptotically consistent estimates of causal effect. Finally, this paper shows GP-SLC is competitive with or more accurate than widely used causal inference techniques such as multi-level linear models and Bayesian additive regression trees. Benchmark datasets include the Infant Health and Development Program and a dataset showing the effect of changing temperatures on state-wide energy consumption across New England.

There has been considerable recent interest in mutual information (MI) minimization for various machine learning tasks. However, estimating and minimizing MI in high-dimensional spaces remains a challenging problem, especially when only samples are accessible, rather than the underlying distribution forms. Previous works mainly focus on MI lower bound approximation, which is not applicable to MI minimization problems. In this paper, we propose a novel Contrastive Log-ratio Upper Bound (CLUB) of mutual information. We provide a theoretical analysis of the properties of CLUB and its variational approximation. Based on this upper bound, we introduce an accelerated MI minimization training scheme, that bridges MI minimization with negative sampling. Simulation studies on Gaussian distributions show that CLUB provides reliable estimates. Real-world MI minimization experiments, including domain adaptation and the information bottleneck, further demonstrate the effectiveness of the proposed method.

We show new connections between adversarial learning and explainability for deep neural networks (DNNs). One form of explanation of the output of a neural network model in terms of its input features, is a vector of feature-attributions, which can be generated by various techniques such as Integrated Gradients (IG), DeepSHAP, LIME, and CXPlain. Two desirable characteristics of an attribution-based explanation are: (1) \textit{sparseness}: the attributions of irrelevant or weakly relevant features should be negligible, thus resulting in \textit{concise} explanations in terms of the significant features, and (2) \textit{stability}: it should not vary significantly within a small local neighborhood of the input. Our first contribution is a theoretical exploration of how these two properties (when using IG-based attributions) are related to adversarial training, for a class of 1-layer networks (which includes logistic regression models for binary and multi-class classification); for these networks we show that (a) adversarial training using an $\ell_\infty$-bounded adversary produces models with sparse attribution vectors, and (b) natural model-training while encouraging stable explanations (via an extra term in the loss function), is equivalent to adversarial training. Our second contribution is an empirical verification of phenomenon (a), which we show, somewhat surprisingly, occurs \textit{not only in 1-layer networks, but also DNNs trained on standard image datasets}, and extends beyond IG-based attributions, to those based on DeepSHAP: adversarial training with $\linf$-bounded perturbations yields significantly sparser attribution vectors, with little degradation in performance on natural test data, compared to natural training. Moreover, the sparseness of the attribution vectors is significantly better than that achievable via $\ell_1$-regularized natural training.

Although Reinforcement Learning (RL) algorithms have found tremendous success in simulated domains, they often cannot directly be applied to physical systems, especially in cases where there are hard constraints to satisfy (e.g. on safety or resources). In standard RL, the agent is incentivized to explore any behavior as long as it maximizes rewards, but in the real world, undesired behavior can damage either the system or the agent in a way that breaks the learning process itself. In this work, we model the problem of learning with constraints as a Constrained Markov Decision Process and provide a new on-policy formulation for solving it. A key contribution of our approach is to translate cumulative cost constraints into state-based constraints. Through this, we define a safe policy improvement method which maximizes returns while ensuring that the constraints are satisfied at every step. We provide theoretical guarantees under which the agent converges while ensuring safety over the course of training. We also highlight the computational advantages of this approach. The effectiveness of our approach is demonstrated on safe navigation tasks and in safety-constrained versions of MuJoCo environments, with deep neural networks.

This paper builds on the connection between graph neural networks and traditional dynamical systems. We propose continuous graph neural networks (CGNN), which generalise existing graph neural networks with discrete dynamics in that they can be viewed as a specific discretisation scheme. The key idea is how to characterise the continuous dynamics of node representations, i.e. the derivatives of node representations, w.r.t. time.Inspired by existing diffusion-based methods on graphs (e.g. PageRank and epidemic models on social networks), we define the derivatives as a combination of the current node representations,the representations of neighbors, and the initial values of the nodes. We propose and analyse two possible dynamics on graphs—including each dimension of node representations (a.k.a. the feature channel) change independently or interact with each other—both with theoretical justification. The proposed continuous graph neural net-works are robust to over-smoothing and hence allow us to build deeper networks, which in turn are able to capture the long-range dependencies between nodes. Experimental results on the task of node classification demonstrate the effectiveness of our proposed approach over competitive baselines.

The F-measure is a widely used performance measure for multi-label classification, where multiple labels can be active in an instance simultaneously (e.g. in image tagging, multiple tags can be active in any image). In particular, the F-measure explicitly balances recall (fraction of active labels predicted to be active) and precision (fraction of labels predicted to be active that are actually so), both of which are important in evaluating the overall performance of a multi-label classifier. As with most discrete prediction problems, however, directly optimizing the F-measure is computationally hard. In this paper, we explore the question of designing convex surrogate losses that are calibrated for the F-measure -- specifically, that have the property that minimizing the surrogate loss yields (in the limit of sufficient data) a Bayes optimal multi-label classifier for the F-measure. We show that the F-measure for an $s$-label problem, when viewed as a $2^s \times 2^s$ loss matrix, has rank at most $s^2+1$, and apply a result of Ramaswamy et al. (2014) to design a family of convex calibrated surrogates for the F-measure. The resulting surrogate risk minimization algorithms can be viewed as decomposing the multi-label F-measure learning problem into $s^2+1$ binary class probability estimation problems. We also provide a quantitative regret transfer bound for our surrogates, which allows any regret guarantees for the binary problems to be transferred to regret guarantees for the overall F-measure problem, and discuss a connection with the algorithm of Dembczynski et al. (2013). Our experiments confirm our theoretical findings.

Invariance (defined in a general sense) has been one of the most effective priors for representation learning. Direct factorization of parametric models is feasible only for a small range of invariances, while regularization approaches, despite improved generality, lead to nonconvex optimization. In this work, we develop a \emph{convex} representation learning algorithm for a variety of generalized invariances that can be modeled as semi-norms. Novel Euclidean embeddings are introduced for kernel representers in a semi-inner-product space, and approximation bounds are established. This allows invariant representations to be learned efficiently and effectively as confirmed in our experiments, along with accurate predictions.

Supervised learning methods excel at capturing statistical properties of language when trained over large text corpora. Yet, these models often produce inconsistent outputs in goal-oriented language settings as they are not trained to complete the underlying task. Moreover, as soon as the agents are finetuned to maximize task completion, they suffer from the so-called language drift phenomenon: they slowly lose syntactic and semantic properties of language as they only focus on solving the task. In this paper, we propose a generic approach to counter language drift called Seeded iterated learning(SIL). We periodically refine a pretrained student agent by imitating data sampled from a newly generated teacher agent. At each time step, the teacher is created by copying the student agent, before being finetuned to maximize task completion.SIL does not require external syntactic constraint nor semantic knowledge, making it a valuable task-agnostic finetuning protocol. We evaluate SIL in a toy-setting Lewis Game, and then scale it up to the translation game with natural language. In both settings, SIL helps counter language drift as well as it improves the task completion compared to baselines.

Deep reinforcement learning (RL) has achieved great empirical successes in various domains. However, the large search space of neural networks requires a large amount of data, which makes the current RL algorithms not sample efficient. Motivated by the fact that many environments with continuous state space have smooth transitions, we propose to learn a smooth policy that behaves smoothly with respect to states. We develop a new framework --- \textbf{S}mooth \textbf{R}egularized \textbf{R}einforcement \textbf{L}earning ($\textbf{SR}^2\textbf{L}$), where the policy is trained with smoothness-inducing regularization. Such regularization effectively constrains the search space, and enforces smoothness in the learned policy. Moreover, our proposed framework can also improve the robustness of policy against measurement error in the state space, and can be naturally extended to distribubutionally robust setting. We apply the proposed framework to both on-policy (TRPO) and off-policy algorithm (DDPG). Through extensive experiments, we demonstrate that our method achieves improved sample efficiency and robustness.

Label smoothing is commonly used in training deep learning models, wherein one-hot training labels are mixed with uniform label vectors. Empirically, smoothing has been shown to improve both predictive performance and model calibration. In this paper, we study whether label smoothing is also effective as a means of coping with label noise. While label smoothing apparently amplifies this problem --- being equivalent to injecting symmetric noise to the labels --- we show how it relates to a general family of loss-correction techniques from the label noise literature. Building on this connection, we show that label smoothing is competitive with loss-correction under label noise. Further, we show that when distilling models from noisy data, label smoothing of the teacher is beneficial; this is in contrast to recent findings for noise-free problems, and sheds further light on settings where label smoothing is beneficial.

The LSTM network was proposed to overcome the difficulty in learning long-term dependence, and has made significant advancements in applications. With its success and drawbacks in mind, this paper raises the question -do RNN and LSTM have long memory? We answer it partially by proving that RNN and LSTM do not have long memory from a statistical perspective. A new definition for long memory networks is further introduced, and it requires the model weights to decay at a polynomial rate. To verify our theory, we convert RNN and LSTM into long memory networks by making a minimal modification, and their superiority is illustrated in modeling longterm dependence of various datasets.

In this paper, we introduce a novel form of value function, $Q(s, s')$, that expresses the utility of transitioning from a state $s$ to a neighboring state $s'$ and then acting optimally thereafter. In order to derive an optimal policy, we develop a forward dynamics model that learns to make next-state predictions that maximize this value. This formulation decouples actions from values while still learning off-policy. We highlight the benefits of this approach in terms of value function transfer, learning within redundant action spaces, and learning off-policy from state observations generated by sub-optimal or completely random policies. Code and videos are available at http://sites.google.com/view/qss-paper.

Estimation of individual treatment effects is commonly used as the basis for contextual decision making in fields such as healthcare, education, and economics. However, it is often sufficient for the decision maker to have estimates of upper and lower bounds on the potential outcomes of decision alternatives to assess risks and benefits. We show that, in such cases, we can improve sample efficiency by estimating simple functions that bound these outcomes instead of estimating their conditional expectations, which may be complex and hard to estimate. Our analysis highlights a trade-off between the complexity of the learning task and the confidence with which the learned bounds hold. Guided by these findings, we develop an algorithm for learning upper and lower bounds on potential outcomes which optimize an objective function defined by the decision maker, subject to the probability that bounds are violated being small. Using a clinical dataset and a well-known causality benchmark, we demonstrate that our algorithm outperforms baselines, providing tighter, more reliable bounds.

The deterministic CUR matrix decomposition is a low-rank approximation method to analyze a data matrix. It has attracted considerable attention due to its high interpretability, which results from the fact that the decomposed matrices consist of subsets of the original columns and rows of the data matrix. The subset is obtained by optimizing an objective function with sparsity-inducing norms via coordinate descent. However, the existing algorithms for optimization incur high computation costs. This is because coordinate descent iteratively updates all the parameters in the objective until convergence. This paper proposes a fast deterministic CUR matrix decomposition. Our algorithm safely skips unnecessary updates by efficiently evaluating the optimality conditions for the parameters to be zeros. In addition, we preferentially update the parameters that must be nonzeros. Theoretically, our approach guarantees the same result as the original approach. Experiments demonstrate that our algorithm speeds up the deterministic CUR while achieving the same accuracy.

We introduce a novel regularization approach for deep learning that incorporates and respects the underlying graphical structure of the neural network. Existing regularization methods often focus on penalizing weights in a global/uniform manner that ignores the connectivity structure of the neural network. We propose to use the Fiedler value of the neural network's underlying graph as a tool for regularization. We provide theoretical support for this approach via spectral graph theory. We show several useful properties of the Fiedler value that makes it suitable for regularization. We provide an approximate, variational approach for faster computation during training. We provide bounds on such approximations. We provide an alternative formulation of this framework in the form of a structurally weighted L1 penalty, thus linking our approach to sparsity induction. We performed experiments on datasets that compare Fiedler regularization with traditional regularization methods such as Dropout and weight decay. Results demonstrate the efficacy of Fiedler regularization.

Building rich machine learning datasets in a scalable manner often necessitates a crowd-sourced data collection pipeline. In this work, we use human studies to investigate the consequences of employing such a pipeline, focusing on the popular ImageNet dataset. We study how specific design choices in the ImageNet creation process impact the fidelity of the resulting dataset---including the introduction of biases that state-of-the-art models exploit. Our analysis pinpoints how a noisy data collection pipeline can lead to a systematic misalignment between the resulting benchmark and the real-world task it serves as a proxy for. Finally, our findings emphasize the need to augment our current model training and evaluation toolkit to take such misalignment into account.

\textbf{G}raph \textbf{C}onvolutional \textbf{N}etwork (\textbf{GCN}) is widely used in graph data learning tasks such as recommendation. However, when facing a large graph, the graph convolution is very computationally expensive thus is simplified in all existing GCNs, yet is seriously impaired due to the oversimplification. To address this gap, we leverage the \textit{original graph convolution} in GCN and propose a \textbf{L}ow-pass \textbf{C}ollaborative \textbf{F}ilter (\textbf{LCF}) to make it applicable to the large graph. LCF is designed to remove the noise caused by exposure and quantization in the observed data, and it also reduces the complexity of graph convolution in an unscathed way. Experiments show that LCF improves the effectiveness and efficiency of graph convolution and our GCN outperforms existing GCNs significantly. Codes are available on \url{https://github.com/Wenhui-Yu/LCFN}.

In this paper, we study the graph classification problem from the graph homomorphism perspective. We consider the homomorphisms from $F$ to $G$, where $G$ is a graph of interest (e.g. molecules or social networks) and $F$ belongs to some family of graphs (e.g. paths or non-isomorphic trees). We show that graph homomorphism numbers provide a natural invariant (isomorphism invariant and $\mathcal{F}$-invariant) embedding maps which can be used for graph classification. Viewing the expressive power of a graph classifier by the $\mathcal{F}$-indistinguishable concept, we prove the universality property of graph homomorphism vectors in approximating $\mathcal{F}$-invariant functions. In practice, by choosing $\mathcal{F}$ whose elements have bounded tree-width, we show that the homomorphism method is efficient compared with other methods.

Formation mechanisms are fundamental to the study of complex networks, but learning them from observations is challenging. In real-world domains, one often has access only to the final constructed graph, instead of the full construction process, and observed graphs exhibit complex structural properties. In this work, we propose GraphOpt, an end-to-end framework that jointly learns an implicit model of graph structure formation and discovers an underlying optimization mechanism in the form of a latent objective function. The learned objective can serve as an explanation for the observed graph properties, thereby lending itself to transfer across different graphs within a domain. GraphOpt poses link formation in graphs as a sequential decision-making process and solves it using maximum entropy inverse reinforcement learning algorithm. Further, it employs a novel continuous latent action space that aids scalability. Empirically, we demonstrate that GraphOpt discovers a latent objective transferable across graphs with different characteristics. GraphOpt also learns a robust stochastic policy that achieves competitive link prediction performance without being explicitly trained on this task and further enables construction of graphs with properties similar to those of the observed graph.

Variance-reduced algorithms, although achieve great theoretical performance, can run slowly in practice due to the periodic gradient estimation with a large batch of data. Batch-size adaptation thus arises as a promising approach to accelerate such algorithms. However, existing schemes either apply prescribed batch-size adaption rule or exploit the information along optimization path via additional backtracking and condition verification steps. In this paper, we propose a novel scheme, which eliminates backtracking line search but still exploits the information along optimization path by adapting the batch size via history stochastic gradients. We further theoretically show that such a scheme substantially reduces the overall complexity for popular variance-reduced algorithms SVRG and SARAH/SPIDER for both conventional nonconvex optimization and reinforcement learning problems. To this end, we develop a new convergence analysis framework to handle the dependence of the batch size on history stochastic gradients. Extensive experiments validate the effectiveness of the proposed batch-size adaptation scheme.

Training neural ODEs on large datasets has not been tractable due to the necessity of allowing the adaptive numerical ODE solver to refine its step size to very small values. In practice this leads to dynamics equivalent to many hundreds or even thousands of layers. In this paper, we overcome this apparent difficulty by introducing a theoretically-grounded combination of both optimal transport and stability regularizations which encourage neural ODEs to prefer simpler dynamics out of all the dynamics that solve a problem well. Simpler dynamics lead to faster convergence and to fewer discretizations of the solver, considerably decreasing wall-clock time without loss in performance. Our approach allows us to train neural ODE-based generative models to the same performance as the unregularized dynamics, with significant reductions in training time. This brings neural ODEs closer to practical relevance in large-scale applications.

We consider the classical problem of sequential probability assignment under logarithmic loss while competing against an arbitrary, potentially nonparametric class of experts. We obtain improved bounds on the minimax regret via a new approach that exploits the self-concordance property of the logarithmic loss. We show that for any expert class with (sequential) metric entropy $\mathcal{O}(\gamma^{-p})$ at scale $\gamma$, the minimax regret is $\mathcal{O}(n^{\frac{p}{p+1}})$, and that this rate cannot be improved without additional assumptions on the expert class under consideration. As an application of our techniques, we resolve the minimax regret for nonparametric Lipschitz classes of experts.

In this paper, we consider the problem of sleeping bandits with stochastic action sets and adversarial rewards. In this setting, in contrast to most work in bandits, the actions may not be available at all times. For instance, some products might be out of stock in item recommendation. The best existing efficient (i.e., polynomial-time) algorithms for this problem only guarantee a $O(T^{2/3})$ upper-bound on the regret. Yet, inefficient algorithms based on EXP4 can achieve $O(\sqrt{T})$. In this paper, we provide a new computationally efficient algorithm inspired by EXP3 satisfying a regret of order $O(\sqrt{T})$ when the availabilities of each action $i \in \cA$ are independent. We then study the most general version of the problem where at each round available sets are generated from some unknown arbitrary distribution (i.e., without the independence assumption) and propose an efficient algorithm with $O(\sqrt {2^K T})$ regret guarantee. Our theoretical results are corroborated with experimental evaluations.

We give the first input-sparsity time algorithms for the rank-$k$ low rank approximation problem in every Schatten norm. Specifically, for a given $n\times n$ matrix $A$, our algorithm computes $Y,Z\in \R^{n\times k}$, which, with high probability, satisfy $\|A-YZ^T\|_p \leq (1+\eps)\|A-A_k\|_p$, where $\|M\|_p = \left (\sum_{i=1}^n \sigma_i(M)^p \right )^{1/p}$ is the Schatten $p$-norm of a matrix $M$ with singular values $\sigma_1(M), \ldots, \sigma_n(M)$, and where $A_k$ is the best rank-$k$ approximation to $A$. Our algorithm runs in time $\tilde{O}(\nnz(A) + n^{\alpha_p}\poly(k/\eps))$, where $\alpha_p = 1$ for $p\in [1,2)$ and $\alpha_p = 1 + (\omega-1)(1-2/p)$ for $p>2$ and $\omega \approx 2.374$ is the exponent of matrix multiplication. For the important case of $p = 1$, which corresponds to the more ``robust'' nuclear norm, we obtain $\tilde{O}(\nnz(A) + n \cdot \poly(k/\epsilon))$ time, which was previously only known for the Frobenius norm $(p = 2)$. Moreover, since $\alpha_p < \omega$ for every $p$, our algorithm has a better dependence on $n$ than that in the singular value decomposition for every $p$. Crucial to our analysis is the use of dimensionality reduction for Ky-Fan $p$-norms.

Robust optimization has been widely used in nowadays data science, especially in adversarial training. However, little research has been done to quantify how robust optimization changes the optimizers and the prediction losses comparing to standard training. In this paper, inspired by the influence function in robust statistics, we introduce the Adversarial Influence Function (AIF) as a tool to investigate the solution produced by robust optimization. The proposed AIF enjoys a closed-form and can be calculated efficiently. To illustrate the usage of AIF, we apply it to study model sensitivity -- a quantity defined to capture the change of prediction losses on the natural data after implementing robust optimization. We use AIF to analyze how model complexity and randomized smoothing affect the model sensitivity with respect to specific models. We further derive AIF for kernel regressions, with a particular application to neural tangent kernels, and experimentally demonstrate the effectiveness of the proposed AIF. Lastly, the theories of AIF will be extended to distributional robust optimization.

Selective rationalization improves neural network interpretability by identifying a small subset of input features — the rationale — that best explains or supports the prediction. A typical rationalization criterion, i.e. maximum mutual information (MMI), finds the rationale that maximizes the prediction performance based only on the rationale. However, MMI can be problematic because it picks up spurious correlations between the input features and the output. Instead, we introduce a game-theoretic invariant rationalization criterion where the rationales are constrained to enable the same predictor to be optimal across different environments. We show both theoretically and empirically that the proposed rationales can rule out spurious correlations and generalize better to different test scenarios. The resulting explanations also align better with human judgments. Our implementations are publicly available at https://github.com/code-terminator/invariant_rationalization.

Survival Analysis and Reliability Theory are concerned with the analysis of time-to-event data, in which observations correspond to waiting times until an event of interest, such as death from a particular disease or failure of a component in a mechanical system. This type of data is unique due to the presence of censoring, a type of missing data that occurs when we do not observe the actual time of the event of interest but instead we have access to an approximation for it given by random interval in which the observation is known to belong.

Most traditional methods are not designed to deal with censoring, and thus we need to adapt them to censored time-to-event data. In this paper, we focus on non-parametric Goodness-of-Fit testing procedures based on combining the Stein's method and kernelized discrepancies. While for uncensored data, there is a natural way of implementing a kernelized Stein discrepancy test, for censored data there are several options, each of them with different advantages and disadvantages. In this paper we propose a collection of kernelized Stein discrepancy tests for time-to-event data, and we study each of them theoretically and empirically. Our experimental results show that our proposed methods perform better than existing tests, including previous tests based on a kernelized maximum mean discrepancy.

The choice of approximate posterior distributions plays a central role in stochastic variational inference (SVI). One effective solution is the use of normalizing flows \cut{defined on Euclidean spaces} to construct flexible posterior distributions. However, one key limitation of existing normalizing flows is that they are restricted to the Euclidean space and are ill-equipped to model data with an underlying hierarchical structure. To address this fundamental limitation, we present the first extension of normalizing flows to hyperbolic spaces. We first elevate normalizing flows to hyperbolic spaces using coupling transforms defined on the tangent bundle, termed Tangent Coupling ($\mathcal{TC}$). We further introduce Wrapped Hyperboloid Coupling ($\mathcal{W}\mathbb{H}C$), a fully invertible and learnable transformation that explicitly utilizes the geometric structure of hyperbolic spaces, allowing for expressive posteriors while being efficient to sample from. We demonstrate the efficacy of our novel normalizing flow over hyperbolic VAEs and Euclidean normalizing flows. Our approach achieves improved performance on density estimation, as well as reconstruction of real-world graph data, which exhibit a hierarchical structure. Finally, we show that our approach can be used to power a generative model over hierarchical data using hyperbolic latent variables.

Retrieving relevant targets from an extremely large target set under computational limits is a common challenge for information retrieval and recommendation systems. Tree models, which formulate targets as leaves of a tree with trainable node-wise scorers, have attracted a lot of interests in tackling this challenge due to their logarithmic computational complexity in both training and testing. Tree-based deep models (TDMs) and probabilistic label trees (PLTs) are two representative kinds of them. Though achieving many practical successes, existing tree models suffer from the training-testing discrepancy, where the retrieval performance deterioration caused by beam search in testing is not considered in training. This leads to an intrinsic gap between the most relevant targets and those retrieved by beam search with even the optimally trained node-wise scorers. We take a first step towards understanding and analyzing this problem theoretically, and develop the concept of Bayes optimality under beam search and calibration under beam search as general analyzing tools for this purpose. Moreover, to eliminate the discrepancy, we propose a novel algorithm for learning optimal tree models under beam search. Experiments on both synthetic and real data verify the rationality of our theoretical analysis and demonstrate the superiority of our algorithm compared to state-of-the-art methods.

In this paper, we address the discovery of robotic options from demonstrations in an unsupervised manner. Specifically, we present a framework to jointly learn low-level control policies and higher-level policies of how to use them from demonstrations of a robot performing various tasks. By representing options as continuous latent variables, we frame the problem of learning these options as latent variable inference. We then present a temporally causal variant of variational inference based on a temporal factorization of trajectory likelihoods, that allows us to infer options in an unsupervised manner. We demonstrate the ability of our framework to learn such options across three robotic demonstration datasets.

Instance- and Label-dependent label Noise (ILN) widely exists in real-world datasets but has been rarely studied. In this paper, we focus on Bounded Instance- and Label-dependent label Noise (BILN), a particular case of ILN where the label noise rates---the probabilities that the true labels of examples flip into the corrupted ones---have upper bound less than $1$. Specifically, we introduce the concept of distilled examples, i.e. examples whose labels are identical with the labels assigned for them by the Bayes optimal classifier, and prove that under certain conditions classifiers learnt on distilled examples will converge to the Bayes optimal classifier. Inspired by the idea of learning with distilled examples, we then propose a learning algorithm with theoretical guarantees for its robustness to BILN. At last, empirical evaluations on both synthetic and real-world datasets show effectiveness of our algorithm in learning with BILN.

Recent successes of game-theoretic formulations in ML have caused a resurgence of research interest in differentiable games. Overwhelmingly, that research focuses on methods and upper bounds on their speed of convergence. In this work, we approach the question of fundamental iteration complexity by providing lower bounds to complement the linear (i.e. geometric) upper bounds observed in the literature on a wide class of problems. We cast saddle-point and min-max problems as 2-player games. We leverage tools from single-objective convex optimisation to propose new linear lower bounds for convex-concave games. Notably, we give a linear lower bound for $n$-player differentiable games, by using the spectral properties of the update operator. We then propose a new definition of the condition number arising from our lower bound analysis. Unlike past definitions, our condition number captures the fact that linear rates are possible in games, even in the absence of strong convexity or strong concavity in the variables.

This paper studies the lower bound complexity for minimax optimization problem whose objective function is the average of $n$ individual smooth convex-concave functions. We consider the algorithm which gets access to gradient and proximal oracle for each individual component. For the strongly-convex-strongly-concave case, we prove such an algorithm can not reach an $\varepsilon$-suboptimal point in fewer than $\Omega\left((n+\kappa)\log(1/\varepsilon)\right)$ iterations, where $\kappa$ is the condition number of the objective function. This lower bound matches the upper bound of the existing incremental first-order oracle algorithm stochastic variance-reduced extragradient. We develop a novel construction to show the above result, which partitions the tridiagonal matrix of classical examples into $n$ groups. This construction is friendly to the analysis of incremental gradient and proximal oracle and we also extend the analysis to general convex-concave cases.

Attention based Transformer architecture has enabled significant advances in the field of natural language processing. In addition to new pre-training techniques, recent improvements crucially rely on working with a relatively larger embedding dimension for tokens. Unfortunately, this leads to models that are prohibitively large to be employed in the downstream tasks. In this paper we identify one of the important factors contributing to the large embedding size requirement. In particular, our analysis highlights that the scaling between the number of heads and the size of each head in the current architecture gives rise to a low-rank bottleneck in attention heads, causing this limitation. We further validate this in our experiments. As a solution we propose to set the head size of an attention unit to input sequence length, and independent of the number of heads, resulting in multi-head attention layers with provably more expressive power. We empirically show that this allows us to train models with a relatively smaller embedding dimension and with better performance scaling.

Generating formal-language programs represented by relational tuples, such as Lisp programs or mathematical operations, to solve problems stated in natural language is a challenging task because it requires explicitly capturing discrete symbolic structural information implicit in the input. However, most general neural sequence models do not explicitly capture such structural information, limiting their performance on these tasks. In this paper, we propose a new encoder-decoder model based on a structured neural representation, Tensor Product Representations (TPRs), for mapping Natural-language problems to Formal-language solutions, called TPN2F. The encoder of TP-N2F employs TPR ‘binding’ to encode natural-language symbolic structure in vector space and the decoder uses TPR ‘unbinding’ to generate, in symbolic space, a sequential program represented by relational tuples, each consisting of a relation (or operation) and a number of arguments. TP-N2F considerably outperforms LSTM-based seq2seq models on two benchmarks and creates new state-of-the-art results. Ablation studies show that improvements can be attributed to the use of structured TPRs explicitly in both the encoder and decoder. Analysis of the learned structures shows how TPRs enhance the interpretability of TP-N2F.

What goals should a multi-goal reinforcement learning agent pursue during training in long-horizon tasks? When the desired (test time) goal distribution is too distant to offer a useful learning signal, we argue that the agent should not pursue unobtainable goals. Instead, it should set its own intrinsic goals that maximize the entropy of the historical achieved goal distribution. We propose to optimize this objective by having the agent pursue past achieved goals in sparsely explored areas of the goal space, which focuses exploration on the frontier of the achievable goal set. We show that our strategy achieves an order of magnitude better sample efficiency than the prior state of the art on long-horizon multi-goal tasks including maze navigation and block stacking.

Humans have the ability to robustly recognize objects with various factors of variations such as nonrigid transformations, background noises, and changes in lighting conditions. However, training deep learning models generally require huge amount of data instances under diverse variations, to ensure its robustness. To alleviate the need of collecting large amount of data and better learn to generalize with scarce data instances, we propose a novel meta-learning method which learns to transfer factors of variations from one class to another, such that it can improve the classification performance on unseen examples. Transferred variations generate virtual samples that augment the feature space of the target class during training, simulating upcoming query samples with similar variations. By sharing the factors of variations across different classes, the model becomes more robust to variations in the unseen examples and tasks using small number of examples per class. We validate our model on multiple benchmark datasets for few-shot classification and face recognition, on which our model significantly improves the performance of the base model, outperforming relevant baselines.

This paper studies the statistical theory of off-policy evaluation with function approximation in batch data reinforcement learning problem. We consider a regression-based fitted Q-iteration method, show that it is equivalent to a model-based method that estimates a conditional mean embedding of the transition operator, and prove that this method is information-theoretically optimal and has nearly minimal estimation error. In particular, by leveraging contraction property of Markov processes and martingale concentration, we establish a finite-sample instance-dependent error upper bound and a nearly-matching minimax lower bound. The policy evaluation error depends sharply on a restricted $\chi^2$-divergence over the function class between the long-term distribution of target policy and the distribution of past data. This restricted $\chi^2$-divergence characterizes the statistical limit of off-policy evaluation and is both instance-dependent and function-class-dependent. Further, we provide an easily computable confidence bound for the policy evaluator, which may be useful for optimistic planning and safe policy improvement.

In this paper we tackle the problem of routing multiple agents in a coordinated manner. This is a complex problem that has a wide range of applications in fleet management to achieve a common goal, such as mapping from a swarm of robots and ride sharing. Traditional methods are typically not designed for realistic environments which contain sparsely connected graphs and unknown traffic, and are often too slow in runtime to be practical. In contrast, we propose a graph neural network based model that is able to perform multi-agent routing based on learned value iteration in a sparsely connected graph with dynamically changing traffic conditions. Moreover, our learned communication module enables the agents to coordinate online and adapt to changes more effectively. We created a simulated environment to mimic realistic mapping performed by autonomous vehicles with unknown minimum edge coverage and traffic conditions; our approach significantly outperforms traditional solvers both in terms of total cost and runtime. We also show that our model trained with only two agents on graphs with a maximum of 25 nodes can easily generalize to situations with more agents and/or nodes.

Multi-Task Learning (MTL) is a well established paradigm for jointly learning models for multiple correlated tasks. Often the tasks conflict, requiring trade-offs between them during optimization. In such cases, multi-objective optimization based MTL methods can be used to find one or more Pareto optimal solutions. A common requirement in MTL applications, that cannot be addressed by these methods, is to find a solution satisfying userspecified preferences with respect to task-specific losses. We advance the state-of-the-art by developing the first gradient-based multi-objective MTL algorithm to solve this problem. Our unique approach combines multiple gradient descent with carefully controlled ascent to traverse the Pareto front in a principled manner, which also makes it robust to initialization. The scalability of our algorithm enables its use in large-scale deep networks for MTL. Assuming only differentiability of the task-specific loss functions, we provide theoretical guarantees for convergence. Our experiments show that our algorithm outperforms the best competing methods on benchmark datasets.

Learning how to predict future events from patterns of past events is difficult when the set of possible event types is large. Training an unrestricted neural model might overfit to spurious patterns. To exploit domain-specific knowledge of how past events might affect an event's present probability, we propose using a temporal deductive database to track structured facts over time. Rules serve to prove facts from other facts and from past events. Each fact has a time-varying state---a vector computed by a neural net whose topology is determined by the fact's provenance, including its experience of past events. The possible event types at any time are given by special facts, whose probabilities are neurally modeled alongside their states. In both synthetic and real-world domains, we show that neural probabilistic models derived from concise Datalog programs improve prediction by encoding appropriate domain knowledge in their architecture.

Deep neural networks have been proven to be vulnerable to the so-called adversarial attacks. Recently there have been efforts to defend such attacks with deep generative models. These defense often predict by inverting the deep generative models rather than simple feedforward propagation. Such defenses are difficult to attack due to obfuscated gradient. In this work, we develop a new gradient approximation attack to break these defenses. The idea is to view the inversion phase as a dynamical system, through which we extract the gradient w.r.t the input by tracing its recent trajectory. An amortized strategy is further developed to accelerate the attack. Experiments show that our attack breaks state-of-the-art defenses (e.g DefenseGAN, ABS) much more effectively than other attacks. Additionally, our empirical results provide insights for understanding the weaknesses of deep generative model-based defenses.

We consider nonconvex-concave minimax problems, $\min_{\mathbf{x}} \max_{\mathbf{y} \in \mathcal{Y}} f(\mathbf{x}, \mathbf{y})$, where $f$ is nonconvex in $\mathbf{x}$ but concave in $\mathbf{y}$ and $\mathcal{Y}$ is a convex and bounded set. One of the most popular algorithms for solving this problem is the celebrated gradient descent ascent (GDA) algorithm, which has been widely used in machine learning, control theory and economics. Despite the extensive convergence results for the convex-concave setting, GDA with equal stepsize can converge to limit cycles or even diverge in a general setting. In this paper, we present the complexity results on two-time-scale GDA for solving nonconvex-concave minimax problems, showing that the algorithm can find a stationary point of the function $\Phi(\cdot) := \max_{\mathbf{y} \in \mathcal{Y}} f(\cdot, \mathbf{y})$ efficiently. To the best our knowledge, this is the first nonasymptotic analysis for two-time-scale GDA in this setting, shedding light on its superior practical performance in training generative adversarial networks (GANs) and other real applications.

A general framework for online learning with partial information is one where feedback graphs specify which losses can be observed by the learner. We study a challenging scenario where feedback graphs vary stochastically with time and, more importantly, where graphs and losses are dependent. This scenario appears in several real-world applications that we describe where the outcome of actions are correlated. We devise a new algorithm for this setting that exploits the stochastic properties of the graphs and that benefits from favorable regret guarantees. We present a detailed theoretical analysis of this algorithm, and also report the result of a series of experiments on real-world datasets, which show that our algorithm outperforms standard baselines for online learning with feedback graphs.

We compare the model-free reinforcement learning with the model-based approaches through the lens of the expressive power of neural networks for policies, Q-functions, and dynamics. We show, theoretically and empirically, that even for one-dimensional continuous state space, there are many MDPs whose optimal Q-functions and policies are much more complex than the dynamics. For these MDPs, model-based planning is a favorable algorithm, because the resulting policies can approximate the optimal policy significantly better than a neural network parameterization can, and model-free or model-based policy optimization rely on policy parameterization. Motivated by the theory, we apply a simple multi-step model-based bootstrapping planner (BOOTS) to bootstrap a weak Q-function into a stronger policy. Empirical results show that applying BOOTS on top of model-based or model-free policy optimization algorithms at the test time improves the performance on benchmark tasks.

Kernel selection for kernel-based methods is prohibitively expensive due to the NP-hard nature of discrete optimization. Since gradient-based optimizers are not applicable due to the lack of a differentiable objective function, many state-of-the-art solutions resort to heuristic search or gradient-free optimization. These approaches, however, require imposing restrictive assumptions on the explorable space of structures such as limiting the active candidate pool, thus depending heavily on the intuition of domain experts. This paper instead proposes \textbf{DTERGENS}, a novel generative search framework that constructs and optimizes a high-performance composite kernel expressions generator. \textbf{DTERGENS} does not restrict the space of candidate kernels and is capable of obtaining flexible length expressions by jointly optimizing a generative termination criterion. We demonstrate that our framework explores more diverse kernels and obtains better performance than state-of-the-art approaches on many real-world predictive tasks.

Recent research has shown that incorporating equivariance into neural network architectures is very helpful, and there have been some works investigating the equivariance of networks under group actions. However, as digital images and feature maps are on the discrete meshgrid, corresponding equivariance-preserving transformation groups are very limited. In this work, we deal with this issue from the connection between convolutions and partial differential operators (PDOs). In theory, assuming inputs to be smooth, we transform PDOs and propose a system which is equivariant to a much more general continuous group, the $n$-dimension Euclidean group. In implementation, we discretize the system using the numerical schemes of PDOs, deriving approximately equivariant convolutions (PDO-eConvs). Theoretically, the approximation error of PDO-eConvs is of the quadratic order. It is the first time that the error analysis is provided when the equivariance is approximate. Extensive experiments on rotated MNIST and natural image classification show that PDO-eConvs perform competitively yet use parameters much more efficiently. Particularly, compared with Wide ResNets, our methods result in better results using only 12.6% parameters.

When predictions support decisions they may influence the outcome they aim to predict. We call such predictions performative; the prediction influences the target. Performativity is a well-studied phenomenon in policy-making that has so far been neglected in supervised learning. When ignored, performativity surfaces as undesirable distribution shift, routinely addressed with retraining. We develop a risk minimization framework for performative prediction bringing together concepts from statistics, game theory, and causality. A conceptual novelty is an equilibrium notion we call performative stability. Performative stability implies that the predictions are calibrated not against past outcomes, but against the future outcomes that manifest from acting on the prediction. Our main results are necessary and sufficient conditions for the convergence of retraining to a performatively stable point of nearly minimal loss. In full generality, performative prediction strictly subsumes the setting known as strategic classification. We thus also give the first sufficient conditions for retraining to overcome strategic feedback effects.

We present a new piecewise linear regression methodology that utilises fitting a \emph{difference of convex} functions (DC functions) to the data. These are functions $f$ that may be represented as the difference $\phi_1 - \phi_2$ for a choice of \emph{convex} functions $\phi_1, \phi_2$. The method proceeds by estimating piecewise-liner convex functions, in a manner similar to max-affine regression, whose difference approximates the data. The choice of the function is regularised by a new seminorm over the class of DC functions that controls the $\ell_\infty$ Lipschitz constant of the estimate. The resulting methodology can be efficiently implemented via Quadratic programming \emph{even in high dimensions}, and is shown to have close to minimax statistical risk. We empirically validate the method, showing it to be practically implementable, and to outperform existing regression methods in accuracy on real-world datasets.

The high sample complexity of reinforcement learning challenges its use in practice. A promising approach is to quickly adapt pre-trained policies to new environments. Existing methods for this policy adaptation problem typically rely on domain randomization and meta-learning, by sampling from some distribution of target environments during pre-training, and thus face difficulty on out-of-distribution target environments. We propose new model-based mechanisms that are able to make online adaptation in unseen target environments, by combining ideas from no-regret online learning and adaptive control. We prove that the approach learns policies in the target environment that can quickly recover trajectories from the source environment, and establish the rate of convergence in general settings. We demonstrate the benefits of our approach for policy adaptation in a diverse set of continuous control tasks, achieving the performance of state-of-the-art methods with much lower sample complexity. Our project website, including code, can be found at https://yudasong.github.io/PADA.

Automating algorithm configuration is growing increasingly necessary as algorithms come with more and more tunable parameters. It is common to tune parameters using machine learning, optimizing algorithmic performance (runtime or solution quality, for example) using a training set of problem instances from the specific domain at hand. We investigate a fundamental question about these techniques: how large should the training set be to ensure that a parameter’s average empirical performance over the training set is close to its expected, future performance? We answer this question for algorithm configuration problems that exhibit a widely-applicable structure: the algorithm's performance as a function of its parameters can be approximated by a “simple” function. We show that if this approximation holds under the L∞-norm, we can provide strong sample complexity bounds, but if the approximation holds only under the Lp-norm for p < ∞, it is not possible to provide meaningful sample complexity bounds in the worst case. We empirically evaluate our bounds in the context of integer programming, obtaining sample complexity bounds that are up to 700 times smaller than the previously best-known bounds.

Exploration is widely regarded as one of the most challenging aspects of reinforcement learning (RL), with many naive approaches succumbing to exponential sample complexity. To isolate the challenges of exploration, we propose the following ``reward-free RL'' framework. In the exploration phase, the agent first collects trajectories from an MDP $M$ without a pre-specified reward function. After exploration, it is tasked with computing a near-policies under the transitions of $\mathcal{M}$ for a collection of given reward functions. This framework is particularly suitable where there are many reward functions of interest, or where the reward function is shaped by an external agent to elicit desired behavior. We give an efficient algorithm that conducts $\widetilde{O}(S^2A\mathrm{poly}(H)/\epsilon^2)$ episodes of exploration, and returns $\epsilon$-suboptimal policies for an arbitrary number of reward functions. We achieve this by finding exploratory policies that jointly visit each ``significant'' state with probability proportional to its maximum visitation probability under any possible policy. Moreover, our planning procedure can be instantiated by any black-box approximate planner, such as value iteration or natural policy gradient. Finally, we give a nearly-matching $\Omega(S^2AH^2/\epsilon^2)$ lower bound, demonstrating the near-optimality of our algorithm in this setting.

Many applications require sparse neural networks due to space or inference time restrictions. There is a large body of work on training dense networks to yield sparse networks for inference, but this limits the size of the largest trainable sparse model to that of the largest trainable dense model. In this paper we introduce a method to train sparse neural networks with a fixed parameter count and a fixed computational cost throughout training, without sacrificing accuracy relative to existing dense-to-sparse training methods. Our method updates the topology of the sparse network during training by using parameter magnitudes and infrequent gradient calculations. We show that this approach requires fewer floating-point operations (FLOPs) to achieve a given level of accuracy compared to prior techniques. We demonstrate state-of-the-art sparse training results on a variety of networks and datasets, including ResNet-50, MobileNets on Imagenet-2012, and RNNs on WikiText-103. Finally, we provide some insights into why allowing the topology to change during the optimization can overcome local minima encountered when the topology remains static.

When tasks change over time, meta-transfer learning seeks to improve the efficiency of learning a new task via both meta-learning and transfer-learning. While the standard attention has been effective in a variety of settings, we question its effectiveness in improving meta-transfer learning since the tasks being learned are dynamic and the amount of context can be substantially smaller. In this paper, using a recently proposed meta-transfer learning model, Sequential Neural Processes (SNP), we first empirically show that it suffers from a similar underfitting problem observed in the functions inferred by Neural Processes. However, we further demonstrate that unlike the meta-learning setting, the standard attention mechanisms are not effective in meta-transfer setting. To resolve, we propose a new attention mechanism, Recurrent Memory Reconstruction (RMR), and demonstrate that providing an imaginary context that is recurrently updated and reconstructed with interaction is crucial in achieving effective attention for meta-transfer learning. Furthermore, incorporating RMR into SNP, we propose Attentive Sequential Neural Processes-RMR (ASNP-RMR) and demonstrate in various tasks that ASNP-RMR significantly outperforms the baselines.

Deep neural networks for natural language processing tasks are vulnerable to adversarial input perturbations. In this paper, we present a versatile language for programmatically specifying string transformations---e.g., insertions, deletions, substitutions, swaps, etc.---that are relevant to the task at hand. We then present an approach to adversarially training models that are robust to such user-defined string transformations. Our approach combines the advantages of search-based techniques for adversarial training with abstraction-based techniques. Specifically, we show how to decompose a set of user-defined string transformations into two component specifications, one that benefits from search and another from abstraction. We use our technique to train models on the AG and SST2 datasets and show that the resulting models are robust to combinations of user-defined transformations mimicking spelling mistakes and other meaning-preserving transformations.

Differentiable physics is a powerful approach to learning and control problems that involve physical objects and environments. While notable progress has been made, the capabilities of differentiable physics solvers remain limited. We develop a scalable framework for differentiable physics that can support a large number of objects and their interactions. To accommodate objects with arbitrary geometry and topology, we adopt meshes as our representation and leverage the sparsity of contacts for scalable differentiable collision handling. Collisions are resolved in localized regions to minimize the number of optimization variables even when the number of simulated objects is high. We further accelerate implicit differentiation of optimization with nonlinear constraints. Experiments demonstrate that the presented framework requires up to two orders of magnitude less memory and computation in comparison to recent particle-based methods. We further validate the approach on inverse problems and control scenarios, where it outperforms derivative-free and model-free baselines by at least an order of magnitude.

Tokenization is the first step of many natural language processing (NLP) tasks and plays an important role for neural NLP models. Tokenizaton method such as byte-pair encoding (BPE), which can greatly reduce the large vocabulary and deal with out-of-vocabulary words, has shown to be effective and is widely adopted for sequence generation tasks. While various tokenization methods exist, there is no common acknowledgement which is the best. In this work, we propose to leverage the mixed representations from different tokenization methods for sequence generation tasks, in order to boost the model performance with unique characteristics and advantages of individual tokenization methods. Specifically, we introduce a new model architecture to incorporate mixed representations and a co-teaching algorithm to better utilize the diversity of different tokenization methods. Our approach achieves significant improvements on neural machine translation (NMT) tasks with six language pairs (e.g., English$\leftrightarrow$German, English$\leftrightarrow$Romanian), as well as an abstractive summarization task.

Datasets containing sensitive information are often sequentially analyzed by many algorithms and, accordingly, a fundamental question in differential privacy is concerned with how the overall privacy bound degrades under composition. To address this question, we introduce a family of analytical and sharp privacy bounds under composition using the Edgeworth expansion in the framework of the recently proposed $f$-differential privacy. In short, whereas the existing composition theorem, for example, relies on the central limit theorem, our new privacy bounds under composition gain improved tightness by leveraging the refined approximation accuracy of the Edgeworth expansion. Our approach is easy to implement and computationally efficient for any number of compositions. The superiority of these new bounds is confirmed by an asymptotic error analysis and an application to quantifying the overall privacy guarantees of noisy stochastic gradient descent used in training private deep neural networks.

Autonomous agents that must exhibit flexible and broad capabilities will need to be equipped with large repertoires of skills. Defining each skill with a manually-designed reward function limits this repertoire and imposes a manual engineering burden. Self-supervised agents that set their own goals can automate this process, but designing appropriate goal setting objectives can be difficult, and often involves heuristic design decisions. In this paper, we propose a formal exploration objective for goal-reaching policies that maximizes state coverage. We show that this objective is equivalent to maximizing goal reaching performance together with the entropy of the goal distribution, where goals correspond to full state observations. To instantiate this principle, we present an algorithm called Skew-Fit for learning a maximum-entropy goal distributions. We prove that, under regularity conditions, Skew-Fit converges to a uniform distribution over the set of valid states, even when we do not know this set beforehand. Our experiments show that combining Skew-Fit for learning goal distributions with existing goal-reaching methods outperforms a variety of prior methods on open-sourced visual goal-reaching tasks. Moreover, we demonstrate that Skew-Fit enables a real-world robot to learn to open a door, entirely from scratch, from pixels, and without any manually-designed reward function.

The goal of Sparse Convex Optimization is to optimize a convex function $f$ under a sparsity constraint $s\leq s^*\gamma$, where $s^*$ is the target number of non-zero entries in a feasible solution (sparsity) and $\gamma\geq 1$ is an approximation factor. There has been a lot of work to analyze the sparsity guarantees of various algorithms (LASSO, Orthogonal Matching Pursuit (OMP), Iterative Hard Thresholding (IHT)) in terms of the Restricted Condition Number $\kappa$. The best known algorithms guarantee to find an approximate solution of value $f(x^*)+\epsilon$ with the sparsity bound of $\gamma = O\left(\kappa\min\left\{\log \frac{f(x^0)-f(x^*)}{\epsilon}, \kappa\right\}\right)$, where $x^*$ is the target solution. We present a new Adaptively Regularized Hard Thresholding (ARHT) algorithm that makes significant progress on this problem by bringing the bound down to $\gamma=O(\kappa)$, which has been shown to be tight for a general class of algorithms including LASSO, OMP, and IHT. This is achieved without significant sacrifice in the runtime efficiency compared to the fastest known algorithms. We also provide a new analysis of OMP with Replacement (OMPR) for general $f$, under the condition $s > s^* \frac{\kappa^2}{4}$, which yields Compressed Sensing bounds under the Restricted Isometry Property (RIP). When compared to other Compressed Sensing approaches, it has the advantage of providing a strong tradeoff between the RIP condition and the solution sparsity, while working for any general function $f$ that meets the RIP condition.

We derive analytical expressions for the generalization performance of kernel regression as a function of the number of training samples using theoretical methods from Gaussian processes and statistical physics. Our expressions apply to wide neural networks due to an equivalence between training them and kernel regression with the Neural Tangent Kernel (NTK). By computing the decomposition of the total generalization error due to different spectral components of the kernel, we identify a new spectral principle: as the size of the training set grows, kernel machines and neural networks fit successively higher spectral modes of the target function. When data are sampled from a uniform distribution on a high-dimensional hypersphere, dot product kernels, including NTK, exhibit learning stages where different frequency modes of the target function are learned. We verify our theory with simulations on synthetic data and MNIST dataset.

A framework based on iterative coordinate minimization (CM) is developed for stochastic convex optimization. Given that exact coordinate minimization is impossible due to the unknown stochastic nature of the objective function, the crux of the proposed optimization algorithm is an optimal control of the minimization precision in each iteration. We establish the optimal precision control and the resulting order-optimal regret performance for strongly convex and separably nonsmooth functions. An interesting finding is that the optimal progression of precision across iterations is independent of the low-dimension CM routine employed, suggesting a general framework for extending low-dimensional optimization routines to high-dimensional problems. The proposed algorithm is amenable to online implementation and inherits the scalability and parallelizability properties of CM for large-scale optimization. Requiring only a sublinear order of message exchanges, it also lends itself well to distributed computing as compared with the alternative approach of coordinate gradient descent.

We develop two new stochastic Gauss-Newton algorithms for solving a class of non-convex stochastic compositional optimization problems frequently arising in practice. We consider both the expectation and finite-sum settings under standard assumptions, and use both classical stochastic and SARAH estimators for approximating function values and Jacobians. In the expectation case, we establish $\BigO{\varepsilon^{-2}}$ iteration-complexity to achieve a stationary point in expectation and estimate the total number of stochastic oracle calls for both function value and its Jacobian, where $\varepsilon$ is a desired accuracy. In the finite sum case, we also estimate $\BigO{\varepsilon^{-2}}$ iteration-complexity and the total oracle calls with high probability. To our best knowledge, this is the first time such global stochastic oracle complexity is established for stochastic Gauss-Newton methods. Finally, we illustrate our theoretical results via two numerical examples on both synthetic and real datasets.

Consequential decision-making incentivizes individuals to strategically adapt their behavior to the specifics of the decision rule. While a long line of work has viewed strategic adaptation as gaming and attempted to mitigate its effects, recent work has instead sought to design classifiers that incentivize individuals to improve a desired quality. Key to both accounts is a cost function that dictates which adaptations are rational to undertake. In this work, we develop a causal framework for strategic adaptation. Our causal perspective clearly distinguishes between gaming and improvement and reveals an important obstacle to incentive design. We prove any procedure for designing classifiers that incentivize improvement must inevitably solve a non-trivial causal inference problem. We show a similar result holds for designing cost functions that satisfy the requirements of previous work. With the benefit of hindsight, our results show much of the prior work on strategic classification is causal modeling in disguise.

We investigate the ability of popular flow models to capture tail-properties of a target density by studying the increasing triangular maps used in these flow methods acting on a tractable source density. We show that the density quantile functions of the source and target density provide a precise characterization of the slope of transformation required to capture tails in a target density. We further show that any Lipschitz-continuous transport map acting on a source density will result in a density with similar tail properties as the source, highlighting the trade-off between the importance of choosing a complex source density and a sufficiently expressive transformation to capture desirable properties of a target density. Subsequently, we illustrate that flow models like Real-NVP, MAF, and Glow as implemented lack the ability to capture a distribution with non-Gaussian tails. We circumvent this problem by proposing tail-adaptive flows consisting of a source distribution that can be learned simultaneously with the triangular map to capture tail-properties of a target density. We perform several synthetic and real-world experiments to complement our theoretical findings.

Recent advancements in Generative Adversarial Networks (GANs) enable the generation of highly realistic images, raising concerns about their misuse for malicious purposes. Detecting these GAN-generated images (GAN-images) becomes increasingly challenging due to the significant reduction of underlying artifacts and specific patterns. The absence of such traces can hinder detection algorithms from identifying GAN-images and transferring knowledge to identify other types of GAN-images as well. In this work, we present the Transferable GAN-images Detection framework T-GD, a robust transferable framework for an effective detection of GAN-images. T-GD is composed of a teacher and a student model that can iteratively teach and evaluate each other to improve the detection performance. First, we train the teacher model on the source dataset and use it as a starting point for learning the target dataset. To train the student model, we inject noise by mixing up the source and target datasets, while constraining the weight variation to preserve the starting point. Our approach is a self-training method, but distinguishes itself from prior approaches by focusing on improving the transferability of GAN-image detection. T-GD achieves high performance on the source dataset by overcoming catastrophic forgetting and effectively detecting state-of-the-art GAN-images with only a small volume of data without any metadata information.

The problem of adversarial examples has shown that modern Neural Network (NN) models could be rather fragile. Among the more established techniques to solve the problem, one is to require the model to be {\it $\epsilon$-adversarially robust} (AR); that is, to require the model not to change predicted labels when any given input examples are perturbed within a certain range. However, it is observed that such methods would lead to standard performance degradation, i.e., the degradation on natural examples. In this work, we study the degradation through the regularization perspective. We identify quantities from generalization analysis of NNs; with the identified quantities we empirically find that AR is achieved by regularizing/biasing NNs towards less confident solutions by making the changes in the feature space (induced by changes in the instance space) of most layers smoother uniformly in all directions; so to a certain extent, it prevents sudden change in prediction w.r.t. perturbations. However, the end result of such smoothing concentrates samples around decision boundaries, resulting in less confident solutions, and leads to worse standard performance. Our studies suggest that one might consider ways that build AR into NNs in a gentler way to avoid the problematic regularization.

We propose a novel type of hybrid model for multi-class classification, which utilizes competing linear models to collaborate with an existing black-box model, promoting transparency in the decision-making process. Our proposed hybrid model, Model-Agnostic Linear Competitors (MALC), brings together the interpretable power of linear models and the good predictive performance of the state-of-the-art black-box models. We formulate the training of a MALC model as a convex optimization problem, optimizing the predictive accuracy and transparency (defined as the percentage of data captured by the linear models) in the objective function. Experiments show that MALC offers more model flexibility for users to balance transparency and accuracy, in contrast to the currently available choice of either a pure black-box model or a pure interpretable model. The human evaluation also shows that more users are likely to choose MALC for this model flexibility compared with interpretable models and black-box models.

Contrastive representation learning has been outstandingly successful in practice. In this work, we identify two key properties related to the contrastive loss: (1) alignment (closeness) of features from positive pairs, and (2) uniformity of the induced distribution of the (normalized) features on the hypersphere. We prove that, asymptotically, the contrastive loss optimizes these properties, and analyze their positive effects on downstream tasks. Empirically, we introduce an optimizable metric to quantify each property. Extensive experiments on standard vision and language datasets confirm the strong agreement between both metrics and downstream task performance. Directly optimizing for these two metrics leads to representations with comparable or better performance at downstream tasks than contrastive learning.

Although SGD with random reshuffle has been widely-used in machine learning applications, there is a limited understanding of how model characteristics affect the convergence of the algorithm. In this work, we introduce model incoherence to characterize the diversity of model characteristics and study its impact on convergence of SGD with random reshuffle \shaocong{under weak strong convexity}. Specifically, {\em minimizer incoherence} measures the discrepancy between the global minimizers of a sample loss and those of the total loss and affects the convergence error of SGD with random reshuffle. In particular, we show that the variable sequence generated by SGD with random reshuffle converges to a certain global minimizer of the total loss under full minimizer coherence. The other {\em curvature incoherence} measures the quality of condition numbers of the sample losses and determines the convergence rate of SGD. With model incoherence, our results show that SGD has a faster convergence rate and smaller convergence error under random reshuffle than those under random sampling, and hence provide justifications to the superior practical performance of SGD with random reshuffle.

Group invariant and equivariant Multilayer Perceptrons (MLP), also known as Equivariant Networks, have achieved remarkable success in learning on a variety of data structures, such as sequences, images, sets, and graphs. Using tools from group theory, this paper proves the universality of a broad class of equivariant MLPs with a single hidden layer. In particular, it is shown that having a hidden layer on which the group acts regularly is sufficient for universal equivariance (invariance). A corollary is unconditional universality of equivariant MLPs for Abelian groups, such as CNNs with a single hidden layer. A second corollary is the universality of equivariant MLPs with a high-order hidden layer, where we give both group-agnostic bounds and means for calculating group-specific bounds on the order of hidden layer that guarantees universal equivariance (invariance).

Sparse principal component analysis (PCA) is a widely-used dimensionality reduction tool in statistics and machine learning. Most methods mentioned in literature are either heuristics for good primal feasible solutions under statistical assumptions or ADMM-type algorithms with stationary/critical points convergence property for the regularized reformulation of sparse PCA. However, none of these methods can efficiently verify the quality of the solutions via comparing current objective values with their dual bounds, especially in model-free case. We propose a new framework that finds out upper (dual) bounds for the sparse PCA within polynomial time via solving a convex integer program (IP). We show that, in the worst-case, the dual bounds provided by the convex IP is within an affine function of the global optimal value. Moreover, in contrast to the semi-definition relaxation, this framework is much easier to scale on large cases. Numerical results on both artificial and real cases are reported to demonstrate the advantages of our method.