In this paper, we study combinatorial pure exploration for dueling bandits (CPE-DB): we have multiple candidates for multiple positions as modeled by a bipartite graph, and in each round we sample a duel of two candidates on one position and observe who wins in the duel, with the goal of finding the best candidate-position matching with high probability after multiple rounds of samples. CPE-DB is an adaptation of the original combinatorial pure exploration for multi-armed bandit (CPE-MAB) problem to the dueling bandit setting. We consider both the Borda winner and the Condorcet winner cases. For Borda winner, we establish a reduction of the problem to the original CPE-MAB setting and design PAC and exact algorithms that achieve both the sample complexity similar to that in the CPE-MAB setting (which is nearly optimal for a subclass of problems) and polynomial running time per round. For Condorcet winner, we first design a fully polynomial time approximation scheme (FPTAS) for the offline problem of finding the Condorcet winner with known winning probabilities, and then use the FPTAS as an oracle to design a novel pure exploration algorithm CAR-Cond with sample complexity analysis. CAR-Cond is the first algorithm with polynomial running time per round for identifying the Condorcet winner in CPE-DB.

Distance metric learning (DML) is to learn a representation space equipped with a metric, such that similar examples are closer than dissimilar examples concerning the metric. The recent success of DNNs motivates many DML losses that encourage the intra-class compactness and inter-class separability. The trade-off between inter-class compactness and inter-class separability shapes the DML representation space by determining how much information of the original inputs to retain. In this paper, we propose a Distance Metric Learning with Joint Representation Diversification (JRD) that allows a better balancing point between intra-class compactness and inter-class separability. Specifically, we propose a Joint Representation Similarity regularizer that captures different abstract levels of invariant features and diversifies the joint distributions of representations across multiple layers. Experiments on three deep DML benchmark datasets demonstrate the effectiveness of the proposed approach.

Domain generalization refers to the task of training a model which generalizes to new domains that are not seen during training. We present CSD (Common Specific Decomposition), for this setting, which jointly learns a common component (which generalizes to new domains) and a domain specific component (which overfits on training domains). The domain specific components are discarded after training and only the common component is retained. The algorithm is extremely simple and involves only modifying the final linear classification layer of any given neural network architecture. We present a principled analysis to understand existing approaches, provide identifiability results of CSD, and study the effect of low-rank on domain generalization. We show that CSD either matches or beats state of the art approaches for domain generalization based on domain erasure, domain perturbed data augmentation, and meta-learning. Further diagnostics on rotated MNIST, where domains are interpretable, confirm the hypothesis that CSD successfully disentangles common and domain specific components and hence leads to better domain generalization; moreover, our code and dataset are publicly available at the following URL: \url{https://github.com/vihari/csd}.

A complementary label (CL) simply indicates an incorrect class of an example, but learning with CLs results in multi-class classifiers that can predict the correct class. Unfortunately, the problem setting only allows a single CL for each example, which notably limits its potential since our labelers may easily identify multiple CLs (MCLs) to one example. In this paper, we propose a novel problem setting to allow MCLs for each example and two ways for learning with MCLs. In the first way, we design two wrappers that decompose MCLs into many single CLs, so that we could use any method for learning with CLs. However, the supervision information that MCLs hold is conceptually diluted after decomposition. Thus, in the second way, we derive an unbiased risk estimator; minimizing it processes each set of MCLs as a whole and possesses an estimation error bound. We further improve the second way into minimizing properly chosen upper bounds. Experiments show that the former way works well for learning with MCLs but the latter is even better.

We introduce a new measure to evaluate the transferability of representations learned by classifiers. Our measure, the Log Expected Empirical Prediction (LEEP), is simple and easy to compute: when given a classifier trained on a source data set, it only requires running the target data set through this classifier once. We analyze the properties of LEEP theoretically and demonstrate its effectiveness empirically. Our analysis shows that LEEP can predict the performance and convergence speed of both transfer and meta-transfer learning methods, even for small or imbalanced data. Moreover, LEEP outperforms recently proposed transferability measures such as negative conditional entropy and H scores. Notably, when transferring from ImageNet to CIFAR100, LEEP can achieve up to 30% improvement compared to the best competing method in terms of the correlations with actual transfer accuracy.

We provide an end-to-end differentially private spectral algorithm for learning LDA, based on matrix/tensor decompositions, and establish theoretical guarantees on utility/consistency of the estimated model parameters. We represent the spectral algorithm as a computational graph. Noise can be injected along the edges of this graph to obtain differential privacy. We identify subsets of edges, named ``configurations'', such that adding noise to all edges in such a subset guarantees differential privacy of the end-to-end spectral algorithm. We characterize the sensitivity of the edges with respect to the input and thus estimate the amount of noise to be added to each edge for any required privacy level. We then characterize the utility loss for each configuration as a function of injected noise. Overall, by combining the sensitivity and utility characterization, we obtain an end-to-end differentially private spectral algorithm for LDA and identify which configurations outperform others under specific regimes. We are the first to achieve utility guarantees under a required level of differential privacy for learning in LDA. We additionally show that our method systematically outperforms differentially private variational inference.

A popular line of recent research incorporates ML advice in the design of online algorithms to improve their performance in typical instances. These papers treat the ML algorithm as a black-box, and redesign online algorithms to take advantage of ML predictions. In this paper, we ask the complementary question: can we redesign ML algorithms to provide better predictions for online algorithms? We explore this question in the context of the classic rent-or-buy problem, and show that incorporating optimization benchmarks in ML loss functions leads to significantly better performance, while maintaining a worst-case adversarial result when the advice is completely wrong. We support this finding both through theoretical bounds and numerical simulations.

We introduce Deep Reasoning Networks (DRNets), an end-to-end framework that combines deep learning with constraint reasoning for solving pattern de-mixing problems, typically in an unsupervised or very-weakly-supervised setting. DRNets exploit problem structure and prior knowledge by tightly combining constraint reasoning with stochastic-gradient-based neural network optimization. Our motivating task is from materials discovery and concerns inferring crystal structures of materials from X-ray diffraction data (Crystal-Structure-Phase-Mapping). Given the complexity of its underlying scientific domain, we start by introducing DRNets on an analogous but much simpler task: de-mixing overlapping hand-written Sudokus (Multi-MNIST-Sudoku). On Multi-MNIST-Sudoku, DRNets almost perfectly recovered the mixed Sudokus' digits, with 100\% digit accuracy, outperforming the supervised state-of-the-art MNIST de-mixing models. On Crystal-Structure-Phase-Mapping, DRNets significantly outperform the state of the art and experts' capabilities, recovering more precise and physically meaningful crystal structures.

The true population-level importance of a variable in a prediction task provides useful knowledge about the underlying data-generating mechanism and can help in deciding which measurements to collect in subsequent experiments. Valid statistical inference on this importance is a key component in understanding the population of interest. We present a computationally efficient procedure for estimating and obtaining valid statistical inference on the \textbf{S}hapley \textbf{P}opulation \textbf{V}ariable \textbf{I}mportance \textbf{M}easure (SPVIM). Although the computational complexity of the true SPVIM scales exponentially with the number of variables, we propose an estimator based on randomly sampling only $\Theta(n)$ feature subsets given $n$ observations. We prove that our estimator converges at an asymptotically optimal rate. Moreover, by deriving the asymptotic distribution of our estimator, we construct valid confidence intervals and hypothesis tests. Our procedure has good finite-sample performance in simulations, and for an in-hospital mortality prediction task produces similar variable importance estimates when different machine learning algorithms are applied.

We consider a new unsupervised learning task of inferring parameters of a multiobjective decision making model, based on a set of observed decisions from the human expert. This setting is important in applications (such as the task of portfolio management) where it may be difficult to obtain the human expert's intrinsic decision making model. We formulate such a learning problem as an inverse multiobjective optimization problem (IMOP) and propose its first sophisticated model with statistical guarantees. Then, we reveal several fundamental connections between IMOP, K-means clustering, and manifold learning. Leveraging these critical insights and connections, we propose two algorithms to solve IMOP through manifold learning and clustering. Numerical results confirm the effectiveness of our model and the computational efficacy of algorithms.

Gating mechanisms are widely used in neural network models, where they allow gradients to backpropagate easily through depth or time. However, their saturation property introduces problems of its own. For example, in recurrent models these gates need to have outputs near 1 to propagate information over long time-delays, which requires them to operate in their saturation regime and hinders gradient-based learning of the gate mechanism. We address this problem by deriving two synergistic modifications to the standard gating mechanism that are easy to implement, introduce no additional hyperparameters, and improve learnability of the gates when they are close to saturation. We show how these changes are related to and improve on alternative recently proposed gating mechanisms such as chrono-initialization and Ordered Neurons. Empirically, our simple gating mechanisms robustly improve the performance of recurrent models on a range of applications, including synthetic memorization tasks, sequential image classification, language modeling, and reinforcement learning, particularly when long-term dependencies are involved.

Although ordinary differential equations (ODEs) provide insights for designing network architectures, its relationship with the non-residual convolutional neural networks (CNNs) is still unclear. In this paper, we present a novel ODE model by adding a damping term. It can be shown that the proposed model can recover both a ResNet and a CNN by adjusting an interpolation coefficient. Therefore, the damped ODE model provides a unified framework for the interpretation of residual and non-residual networks. The Lyapunov analysis reveals better stability of the proposed model, and thus yields robustness improvement of the learned networks. Experiments on a number of image classification benchmarks show that the proposed model substantially improves the accuracy of ResNet and ResNeXt over the perturbed inputs from both stochastic noise and adversarial attack methods. Moreover, the loss landscape analysis demonstrates the improved robustness of our method along the attack direction.

In real world, our datasets often contain outliers. Most existing algorithms for handling outliers take high time complexities ({\em e.g.} quadratic or cubic complexity). {\em Coreset} is a popular approach for compressing data so as to speed up the optimization algorithms. However, the current coreset methods cannot be easily extended to handle the case with outliers. In this paper, we propose a new variant of coreset technique, {\em layered sampling}, to deal with two fundamental robust optimization problems: {\em $k$-median/means clustering with outliers} and {\em linear regression with outliers}. This new coreset method is in particular suitable to speed up the iterative algorithms (which often improve the solution within a local range) for those robust optimization problems.

In face recognition, designing margin-based (\textit{e.g.}, angular, additive, additive angular margins) softmax loss functions plays an important role to learn discriminative features. However, these hand-crafted heuristic methods may be sub-optimal because they require much effort to explore the large design space. Recently, an AutoML for loss function search method AM-LFS has been derived, which leverages reinforcement learning to search loss functions during the training process. But its search space is complex and unstable that hindering its superiority. In this paper, we first analyze that the key to enhance the feature discrimination is actually \textbf{how to reduce the softmax probability}. We then design a unified formulation for the current margin-based softmax losses. Accordingly, we define a novel search space and develop a reward-guided search method to automatically obtain the best candidate. Experimental results on a variety of face recognition benchmarks have demonstrated the effectiveness of our method over the state-of-the-art alternatives.

Distribution shift is a major obstacle to the deployment of current deep learning models on real-world problems. Let $Y$ be the class label and $X$ the features. We focus on one type of distribution shift, \textit{ label shift}, where the label marginal distribution $P_Y$ changes but the conditional distribution $P_{X|Y}$ does not. Most existing methods estimate the density ratio between the source- and target-domain label distributions by density matching. However, these methods are either computationally infeasible for large-scale data or restricted to shift correction for discrete labels. In this paper, we propose an end-to-end Label Transformation Framework (LTF) for correcting label shift, which implicitly models the shift of $P_Y$ and the conditional distribution $P_{X|Y}$ using neural networks. Thanks to the flexibility of deep networks, our framework can handle continuous, discrete, and even multi-dimensional labels in a unified way and is scalable to large data. Moreover, for high dimensional $X$, such as images, we find that the redundant information in $X$ severely degrades the estimation accuracy. To remedy this issue, we propose to match the distribution implied by our generative model and the target-domain distribution in a low-dimensional feature space that discards information irrelevant to $Y$. Both theoretical and empirical studies demonstrate the superiority of our method over previous approaches.

This work proposes a progressive manifold identification approach for distributed optimization with sound theoretical justifications to greatly reduce both the rounds of communication and the bytes communicated per round for partly-smooth regularized problems such as the L1- and group-LASSO-regularized ones. Our two-stage method first uses an inexact proximal quasi-Newton method to iteratively identify a sequence of low-dimensional manifolds in which the final solution would lie, and restricts the model update within the current manifold to gradually lower the order of the per-round communication cost from the problem dimension to the dimension of the manifold that contains a solution and makes the problem within it smooth. After identifying this manifold, we take superlinear-convergent truncated semismooth Newton steps computed by preconditioned conjugate gradient to largely reduce the communication rounds by improving the convergence rate from the existing linear or sublinear ones to a superlinear rate. Experiments show that our method can be two orders of magnitude better in the communication cost and an order of magnitude faster in the running time than state of the art.

While successful in many fields, deep neural networks (DNNs) still suffer from some open problems such as bad local minima and unsatisfactory generalization performance. In this work, we propose a novel architecture called Maximum-and-Concatenation Networks (MCN) to try eliminating bad local minima and improving generalization ability as well. Remarkably, we prove that MCN has a very nice property; that is, every local minimum of an (l+1)-layer MCN can be better than, at least as good as, the global minima of the network consisting of its first l layers. In other words, by increasing the network depth, MCN can autonomously improve its local minima's goodness, what is more, it is easy to plug MCN into an existing deep model to make it also have this property. Finally, under mild conditions, we show that MCN can approximate certain continuous function arbitrarily well with high efficiency; that is, the covering number of MCN is much smaller than most existing DNNs such as deep ReLU. Based on this, we further provide a tight generalization bound to guarantee the inference ability of MCN when dealing with testing samples.

With the rapid adoption of machine learning systems in sensitive applications, there is an increasing need to make black-box models explainable. Often we want to identify an influential group of training samples in a particular test prediction for a given machine learning model. Existing influence functions tackle this problem by using first-order approximations of the effect of removing a sample from the training set on model parameters. To compute the influence of a group of training samples (rather than an individual point) in model predictions, the change in optimal model parameters after removing that group from the training set can be large. Thus, in such cases, the first-order approximation can be loose. In this paper, we address this issue and propose second-order influence functions for identifying influential groups in test-time predictions. For linear models, across different sizes and types of groups, we show that using the proposed second-order influence function improves the correlation between the computed influence values and the ground truth ones. We also show that second-order influence functions could be used with optimization techniques to improve the selection of the most influential group for a test-sample.

The variational autoencoder (VAE) can learn the manifold of natural images on certain datasets, as evidenced by meaningful interpolating or extrapolating in the continuous latent space. However, on discrete data such as text, it is unclear if unsupervised learning can discover similar latent space that allows controllable manipulation. In this work, we find that sequence VAEs trained on text fail to properly decode when the latent codes are manipulated, because the modified codes often land in holes or vacant regions in the aggregated posterior latent space, where the decoding network fails to generalize. Both as a validation of the explanation and as a fix to the problem, we propose to constrain the posterior mean to a learned probability simplex, and performs manipulation within this simplex. Our proposed method mitigates the latent vacancy problem and achieves the first success in unsupervised learning of controllable representations for text. Empirically, our method outperforms unsupervised baselines and strong supervised approaches on text style transfer. On automatic evaluation metrics used in text style transfer, even with the decoding network trained from scratch, our method achieves comparable results with state-of-the-art supervised approaches leveraging large-scale pre-trained models for generation. Furthermore, it is capable of performing more flexible fine-grained control over text generation than existing methods.

Most recommender systems (RS) research assumes that a user's utility can be maximized independently of the utility of the other agents (e.g., other users, content providers). In realistic settings, this is often not true -- the dynamics of an RS ecosystem couple the long-term utility of all agents. In this work, we explore settings in which content providers cannot remain viable unless they receive a certain level of user engagement. We formulate this problem as one of equilibrium selection in the induced dynamical system, and show that it can be solved as an optimal constrained matching problem. Our model ensures the system reaches an equilibrium with maximal social welfare supported by a sufficiently diverse set of viable providers. We demonstrate that even in a simple, stylized dynamical RS model, the standard myopic approach to recommendation - always matching a user to the best provider - performs poorly. We develop several scalable techniques to solve the matching problem, and also draw connections to various notions of user regret and fairness, arguing that these outcomes are fairer in a utilitarian sense.

Game-theoretic formulations of feature importance have become popular as a way to "explain" machine learning models. These methods define a cooperative game between the features of a model and distribute influence among these input elements using some form of the game's unique Shapley values. Justification for these methods rests on two pillars: their desirable mathematical properties, and their applicability to specific motivations for explanations. We show that mathematical problems arise when Shapley values are used for feature importance and that the solutions to mitigate these necessarily induce further complexity, such as the need for causal reasoning. We also draw on additional literature to argue that Shapley values do not provide explanations which suit human-centric goals of explainability.

Randomized smoothing is the current state-of-the-art defense with provable robustness against $\ell_2$ adversarial attacks. Many works have devised new randomized smoothing schemes for other metrics, such as $\ell_1$ or $\ell_\infty$; however, substantial effort was needed to derive such new guarantees. This begs the question: can we find a general theory for randomized smoothing? We propose a novel framework for devising and analyzing randomized smoothing schemes, and validate its effectiveness in practice. Our theoretical contributions are: (1) we show that for an appropriate notion of "optimal", the optimal smoothing distributions for any "nice" norms have level sets given by the norm's *Wulff Crystal*; (2) we propose two novel and complementary methods for deriving provably robust radii for any smoothing distribution; and, (3) we show fundamental limits to current randomized smoothing techniques via the theory of *Banach space cotypes*. By combining (1) and (2), we significantly improve the state-of-the-art certified accuracy in $\ell_1$ on standard datasets. Meanwhile, we show using (3) that with only label statistics under random input perturbations, randomized smoothing cannot achieve nontrivial certified accuracy against perturbations of $\ell_p$-norm $\Omega(\min(1, d^{\frac{1}{p} - \frac{1}{2}}))$, when the input dimension $d$ is large. We provide code in github.com/tonyduan/rs4a.

Deep semi-supervised learning (SSL) has been recently shown very effectively. However, its performance is seriously decreased when the class distribution is mismatched, among which a common situation is that unlabeled data contains some classes not seen in the labeled data. Efforts on this issue remain to be limited. This paper proposes a simple and effective safe deep SSL method to alleviate the harm caused by it. In theory, the result learned from the new method is never worse than learning from merely labeled data, and it is theoretically guaranteed that its generalization approaches the optimal in the order $O(\sqrt{d\ln(n)/n})$, even faster than the convergence rate in supervised learning associated with massive parameters. In the experiment of benchmark data, unlike the existing deep SSL methods which are no longer as good as supervised learning in 40\% of unseen-class unlabeled data, the new method can still achieve performance gain in more than 60\% of unseen-class unlabeled data. Moreover, the proposal is suitable for many deep SSL algorithms and can be easily extended to handle other cases of class distribution mismatch.

Sample selection approaches are popular in robust learning from noisy labels. However, how to properly control the selection process so that deep networks can benefit from the memorization effect is a hard problem. In this paper, motivated by the success of automated machine learning (AutoML), we model this issue as a function approximation problem. Specifically, we design a domain-specific search space based on general patterns of the memorization effect and propose a novel Newton algorithm to solve the bi-level optimization problem efficiently. We further provide a theoretical analysis of the algorithm, which ensures a good approximation to critical points. Experiments are performed on both benchmark and real-world data sets. Results demonstrate that the proposed method is much better than the state-of-the-art noisy-label-learning approaches, and also much more efficient than existing AutoML algorithms.

Graph convolutional networks (GCNs) are a powerful deep learning approach for graph-structured data. Recently, GCNs and subsequent variants have shown superior performance in various application areas on real-world datasets. Despite their success, most of the current GCN models are shallow, due to the {\em over-smoothing} problem. In this paper, we study the problem of designing and analyzing deep graph convolutional networks. We propose the GCNII, an extension of the vanilla GCN model with two simple yet effective techniques: {\em Initial residual} and {\em Identity mapping}. We provide theoretical and empirical evidence that the two techniques effectively relieves the problem of over-smoothing. Our experiments show that the deep GCNII model outperforms the state-of-the-art methods on various semi- and full-supervised tasks.

This paper is concerned with statistical estimation of two preferential attachment models: the Buckley-Osthus model and the block preferential attachment model. We prove that the maximum likelihood estimates for both models are consistent. We perform simulation studies to corroborate our theoretical findings. We also apply both models to study the evolution of a real-world network. A list of open problems are presented.

We propose Zeno++, a new robust asynchronous Stochastic Gradient Descent(SGD) procedure, intended to tolerate Byzantine failures of workers. In contrast to previous work, Zeno++ removes several unrealistic restrictions on worker-server communication, now allowing for fully asynchronous updates from anonymous workers, for arbitrarily stale worker updates, and for the possibility of an unbounded number of Byzantine workers. The key idea is to estimate the descent of the loss value after the candidate gradient is applied, where large descent values indicate that the update results in optimization progress. We prove the convergence of Zeno++ for non-convex problems under Byzantine failures. Experimental results show that Zeno++ outperforms existing Byzantine-tolerant asynchronous SGD algorithms.

In this contribution, we augment the metric learning setting by introducing a parametric pseudo-distance, trained jointly with the encoder. Several interpretations are thus drawn for the learned distance-like model's output. We first show it approximates a likelihood ratio which can be used for hypothesis tests, and that it further induces a large divergence across the joint distributions of pairs of examples from the same and from different classes. Evaluation is performed under the verification setting consisting of determining whether sets of examples belong to the same class, even if such classes are novel and were never presented to the model during training. Empirical evaluation shows such method defines an end-to-end approach for the verification problem, able to attain better performance than simple scorers such as those based on cosine similarity and further outperforming widely used downstream classifiers. We further observe training is much simplified under the proposed approach compared to metric learning with actual distances, requiring no complex scheme to harvest pairs of examples.

Recent convolutional neural networks (CNNs) have led to impressive performance but often suffer from poor calibration. They tend to be overconfident, with the model confidence not always reflecting the underlying true ambiguity and hardness. In this paper, we propose angular visual hardness (AVH), a score given by the normalized angular distance between the sample feature embedding and the target classifier to measure sample hardness. We validate this score with an in-depth and extensive scientific study, and observe that CNN models with the highest accuracy also have the best AVH scores. This agrees with an earlier finding that state-of-art models improve on the classification of harder examples. We observe that the training dynamics of AVH is vastly different compared to the training loss. Specifically, AVH quickly reaches a plateau for all samples even though the training loss keeps improving. This suggests the need for designing better loss functions that can target harder examples more effectively. We also find that AVH has a statistically significant correlation with human visual hardness. Finally, we demonstrate the benefit of AVH to a variety of applications such as self-training for domain adaptation and domain generalization.

We study the problem of estimating the distribution of effect sizes (the mean of the test statistic under the alternate hypothesis) in a multiple testing setting. Knowing this distribution allows us to calculate the power (type II error) of any experimental design. We show that it is possible to estimate this distribution using an inexpensive pilot experiment, which takes significantly fewer samples than would be required by an experiment that identified the discoveries. Our estimator can be used to guarantee the number of discoveries that will be made using a given experimental design in a future experiment. We prove that this simple and computationally efficient estimator enjoys a number of favorable theoretical properties, and demonstrate its effectiveness on data from a gene knockout experiment on influenza inhibition in Drosophila.

This paper presents a framework of successive functional gradient optimization for training nonconvex models such as neural networks, where training is driven by mirror descent in a function space. We provide a theoretical analysis and empirical study of the training method derived from this framework. It is shown that the method leads to better performance than that of standard training techniques.

Deep models, while being extremely flexible and accurate, are surprisingly vulnerable to ``small, imperceptible'' perturbations known as adversarial attacks. While the majority of existing attacks focuses on measuring perturbations under the $\ell_p$ metric, Wasserstein distance, which takes geometry in pixel space into account, has long known to be a better metric for measuring image quality and has recently risen as a compelling alternative to the $\ell_p$ metric in adversarial attacks. However, constructing an effective attack under the Wasserstein metric is computationally much more challenging and calls for better optimization algorithms. We address this gap in two ways: (a) we develop an exact yet efficient projection operator to enable a stronger projected gradient attack; (b) we show for the first time that Frank-Wolfe method equipped with a suitable linear minimization oracle works extremely fast under Wasserstein constraints. Our algorithms not only converge faster but also generate much stronger attacks. For instance, we decrease the accuracy of a residual network on CIFAR-10 to $3.4\%$ within a Wasserstein perturbation ball of radius $0.005$, in contrast to $65.5\%$ using the previous state-of-the-art attack based on approximate projection. We show that applying our stronger attacks in adversarial training significantly improves the robustness of adversarially trained models.

Autoregressive (AR) models have been the dominating approach to conditional sequence generation, but are suffering from the issue of high inference latency. Non-autoregressive (NAR) models have been recently proposed to reduce the latency by generating all output tokens in parallel but could only achieve inferior accuracy compared to their autoregressive counterparts, primarily due to a difficulty in dealing with the multi-modality in sequence generation. This paper proposes a new approach that jointly optimizes both AR and NAR models in a unified Expectation-Maximization (EM) framework. In the E-step, an AR model learns to approximate the regularized posterior of the NAR model. In the M-step, the NAR model is updated on the new posterior and selects the training examples for the next AR model. This iterative process can effectively guide the system to remove the multi-modality in the output sequences. To our knowledge, this is the first EM approach to NAR sequence generation. We evaluate our method on the task of machine translation. Experimental results on benchmark data sets show that the proposed approach achieves competitive, if not better, performance with existing NAR models and significantly reduces the inference latency.

We consider the batch reinforcement learning problem where the agent needs to learn only from a fixed batch of data, without further interaction with the environment. In such a scenario, we want to prevent the optimized policy from deviating too much from the data collection policy since the estimation becomes highly unstable otherwise due to the off-policy nature of the problem. However, imposing this requirement too strongly will result in a policy that merely follows the data collection policy. Unlike prior work where this trade-off is controlled by hand-tuned hyperparameters, we propose a novel batch reinforcement learning approach, batch optimization of policy and hyperparameter (BOPAH), that uses a gradient-based optimization of the hyperparameter using held-out data. We show that BOPAH outperforms other batch reinforcement learning algorithms in tabular and continuous control tasks, by finding a good balance to the trade-off between adhering to the data collection policy and pursuing the possible policy improvement.

We study the question of how to aggregate controllers for dynamical systems in order to improve their performance. To this end, we propose a framework of boosting for online control. Our main result is an efficient boosting algorithm that combines weak controllers into a provably more accurate one. Empirical evaluation on a host of control settings supports our theoretical findings.

When presented with Out-of-Distribution (OOD) examples, deep neural networks yield confident, incorrect predictions; detecting OOD examples is challenging, and the potential risks are high. In this paper, we propose to detect OOD examples by identifying inconsistencies between activity patterns and predicted class. We find that characterizing activity patterns by Gram matrices and identifying anomalies in Gram matrix values can yield high OOD detection rates. We identify anomalies in the Gram matrices by simply comparing each value with its respective range observed over the training data. Unlike many approaches, this can be used with any pre-trained softmax classifier and neither requires access to OOD data for fine-tuning hyperparameters, nor does it require OOD access for inferring parameters. We empirically demonstrate applicability across a variety of architectures and vision datasets and, for the important and surprisingly hard task of detecting far out-of-distribution examples, it generally performs better than or equal to state-of-the-art OOD detection methods (including those that do assume access to OOD examples).

We study the basic operation of set union in the global model of differential privacy. In this problem, we are given a universe $U$ of items, possibly of infinite size, and a database $D$ of users. Each user $i$ contributes a subset $W_i \subseteq U$ of items. We want an ($\epsilon$,$\delta$)-differentially private Algorithm which outputs a subset $S \subset \cup_i W_i$ such that the size of $S$ is as large as possible. The problem arises in countless real world applications, and is particularly ubiquitous in natural language processing (NLP) applications. For example, discovering words, sentences, $n$-grams etc., from private text data belonging to users is an instance of the set union problem. In this paper we design new algorithms for this problem that significantly outperform the best known algorithms.

In distributed online optimization over a computing network with heterogeneous nodes, slow nodes can adversely affect the progress of fast nodes, leading to drastic slowdown of the overall convergence process. To address this issue, we consider a new algorithm termed Distributed Any-Batch Mirror Descent (DABMD), which is based on distributed Mirror Descent but uses a fixed per-round computing time to limit the waiting by fast nodes to receive information updates from slow nodes. DABMD is characterized by varying minibatch sizes across nodes. It is applicable to a broader range of problems compared with existing distributed online optimization methods such as those based on dual averaging, and it accommodates time-varying network topology. We study two versions of DABMD, depending on whether the computing nodes average their primal variables via single or multiple consensus iterations. We show that both versions provide strong theoretical performance guarantee, by deriving upperbounds on their expected dynamic regret, which capture the variability in minibatch sizes. Our experimental results show substantial reduction in cost and acceleration in convergence compared with the known best alternative.

We develop a a new polynomial-time algorithm for identification of structural coefficients in linear causal models that subsumes previous state-of-the-art methods, unifying several disparate approaches to identification in this setting. Building on these results, we develop a procedure for identifying total causal effects in linear systems.

The performance of standard learning procedures has been observed to differ widely across groups. 
Recent studies usually attribute this loss discrepancy to an information deficiency for one group (e.g., one group has less data). 
In this work, we point to a more subtle source of loss discrepancy---feature noise. 
Our main result is that even when there is no information deficiency specific to one group (e.g., both groups have infinite data), adding the same amount of feature noise to all individuals leads to loss discrepancy.
For linear regression, we thoroughly characterize the effect of feature noise on loss discrepancy in terms of the amount of noise, the difference between moments of the two groups, and whether group information is used or not.
We then show this loss discrepancy does not vanish immediately if a shift in distribution causes the groups to have similar moments. 
On three real-world datasets, we show feature noise increases the loss discrepancy if groups have different distributions, while it does not affect the loss discrepancy on datasets that groups have similar distributions.

In this paper, we investigate a Lyapunov-like differential inequality that allows us to establish finite-time stability of a continuous-time state-space dynamical system represented via a multivariate ordinary differential equation or differential inclusion. Equipped with this condition, we successfully synthesize first and second-order dynamical systems that achieve finite-time convergence to the minima of a given sufficiently regular cost function. As a byproduct, we show that the p-rescaled gradient flow (p-RGF) proposed by Wibisono et al. (2016) is indeed finite-time convergent, provided the cost function is gradient dominated of order q in (1,p). Thus, we effectively bridge a gap between the p-RGF and the normalized gradient flow (NGF) (p=\infty) proposed by Cortes (2006) in his seminal paper in the context of multi-agent systems. We discuss strategies to discretize our proposed flows and conclude by conducting some numerical experiments to illustrate our results.

Convolutional Neural Networks (CNNs) are known to rely more on local texture rather than global shape when making decisions. Recent work also indicates a close relationship between CNN's texture-bias and its robustness against distribution shift, adversarial perturbation, random corruption, etc. In this work, we attempt at improving various kinds of robustness universally by alleviating CNN's texture bias. With inspiration from the human visual system, we propose a light-weight model-agnostic method, namely Informative Dropout (InfoDrop), to improve interpretability and reduce texture bias. Specifically, we discriminate texture from shape based on local self-information in an image, and adopt a Dropout-like algorithm to decorrelate the model output from the local texture. Through extensive experiments, we observe enhanced robustness under various scenarios (domain generalization, few-shot classification, image corruption, and adversarial perturbation). To the best of our knowledge, this work is one of the earliest attempts to improve different kinds of robustness in a unified model, shedding new light on the relationship between shape-bias and robustness, also on new approaches to trustworthy machine learning algorithms. Code is available at https://github.com/bfshi/InfoDrop.

The standard risk minimization paradigm of machine learning is brittle when operating in environments whose test distributions are different from the training distribution due to spurious correlations. Training on data from many environments and finding invariant predictors reduces the effect of spurious features by concentrating models on features that have a causal relationship with the outcome. In this work, we pose such invariant risk minimization as finding the Nash equilibrium of an ensemble game among several environments. By doing so, we develop a simple training algorithm that uses best response dynamics and, in our experiments, yields similar or better empirical accuracy with much lower variance than the challenging bi-level optimization problem of Arjovsky et al. (2019). One key theoretical contribution is showing that the set of Nash equilibria for the proposed game are equivalent to the set of invariant predictors for any finite number of environments, even with nonlinear classifiers and transformations. As a result, our method also retains the generalization guarantees to a large set of environments shown in Arjovsky et al. (2019). The proposed algorithm adds to the collection of successful game-theoretic machine learning algorithms such as generative adversarial networks.

We study local SGD (also known as parallel SGD and federated SGD), a natural and frequently used distributed optimization method. Its theoretical foundations are currently lacking and we highlight how all existing error guarantees in the convex setting are dominated by a simple baseline, minibatch SGD. (1) For quadratic objectives we prove that local SGD strictly dominates minibatch SGD and that accelerated local SGD is minmax optimal for quadratics; (2) For general convex objectives we provide the first guarantee that at least \emph{sometimes} improves over minibatch SGD, but our guarantee does not always improve over, nor even match, minibatch SGD; (3) We show that indeed local SGD does \emph{not} dominate minibatch SGD by presenting a lower bound on the performance of local SGD that is worse than the minibatch SGD guarantee.

We consider the task of learning in episodic finite-horizon Markov decision processes with an unknown transition function, bandit feedback, and adversarial losses. We propose an efficient algorithm that achieves O(√L|X|AT ) regret with high probability, where L is the horizon, |X| the number of states, |A| the number of actions, and T the number of episodes. To our knowledge, our algorithm is the first to ensure O(√T) regret in this challenging setting; in fact, it achieves the same regret as (Rosenberg & Mansour, 2019a) who consider the easier setting with full-information. Our key contributions are two-fold: a tighter confidence set for the transition function; and an optimistic loss estimator that is inversely weighted by an "upper occupancy bound".

Machine learning (ML) systems often encounter Out-of-Distribution (OoD) errors when dealing with testing data coming from a distribution different from training data. It becomes important for ML systems in critical applications to accurately quantify its predictive uncertainty and screen out these anomalous inputs. However, existing OoD detection approaches are prone to errors and even sometimes assign higher likelihoods to OoD samples. Unlike standard learning tasks, there is currently no well established guiding principle for designing OoD detection architectures that can accurately quantify uncertainty. To address these problems, we first seek to identify guiding principles for designing uncertainty-aware architectures, by proposing Neural Architecture Distribution Search (NADS). NADS searches for a distribution of architectures that perform well on a given task, allowing us to identify common building blocks among all uncertainty-aware architectures. With this formulation, we are able to optimize a stochastic OoD detection objective and construct an ensemble of models to perform OoD detection. We perform multiple OoD detection experiments and observe that our NADS performs favorably, with up to 57% improvement in accuracy compared to state-of-the-art methods among 15 different testing configurations.

Probabilistic clustering models (or equivalently, mixture models) are basic building blocks in countless statistical models and involve latent random variables over discrete spaces. For these models, posterior inference methods can be inaccurate and/or very slow. In this work we introduce deep network architectures trained with labeled samples from any generative model of clustered datasets. At test time, the networks generate approximate posterior samples of cluster labels for any new dataset of arbitrary size. We develop two complementary approaches to this task, requiring either O(N) or O(K) network forward passes per dataset, where N is the dataset size and K the number of clusters. Unlike previous approaches, our methods sample the labels of all the data points from a well-defined posterior, and can learn nonparametric Bayesian posteriors since they do not limit the number of mixture components. As a scientific application, we present a novel approach to neural spike sorting for high-density multielectrode arrays.

This paper investigates the impact of pre-existing offline data on online learning, in the context of dynamic pricing. We study a single-product dynamic pricing problem over a selling horizon of T periods. The demand in each period is determined by the price of the product according to a linear demand model with unknown parameters. We assume that the seller already has some pre-existing offline data before the start of the selling horizon. The seller wants to utilize both the pre-existing offline data and the sequential online data to minimize the regret of the online learning process. We characterize the joint effect of the size, location and dispersion of the offline data on the optimal regret of the online learning process. Our results reveal surprising transformations of the optimal regret rate with respect to the size of the offline data, which we refer to as phase transitions. In addition, our results demonstrate that the location and dispersion of the offline data also have an intrinsic effect on the optimal regret, and we quantify this effect via the inverse-square law.

It is well known that the standard greedy algorithm guarantees a worst-case approximation factor of $1-1/e$ when maximizing a monotone submodular function under a cardinality constraint. However, empirical studies show that its performance is substantially better in practice. This raises a natural question of explaining this improved performance of the greedy algorithm. In this work, we define sharpness for submodular functions as a candidate explanation for this phenomenon. We show that the greedy algorithm provably performs better as the sharpness of the submodular function increases. This improvement ties in closely with the faster convergence rates of first order methods for sharp functions in convex optimization.

It is common practice in deep learning to use overparameterized networks and train for as long as possible; there are numerous studies that show, both theoretically and empirically, that such practices surprisingly do not unduly harm the generalization performance of the classifier. In this paper, we empirically study this phenomenon in the setting of adversarially trained deep networks, which are trained to minimize the loss under worst-case adversarial perturbations. We find that overfitting to the training set does in fact harm robust performance to a very large degree in adversarially robust training across multiple datasets (SVHN, CIFAR-10, CIFAR-100, and ImageNet) and perturbation models (L-infinity and L-2). Based upon this observed effect, we show that the performance gains of virtually all recent algorithmic improvements upon adversarial training can be matched by simply using early stopping. We also show that effects such as the double descent curve do still occur in adversarially trained models, yet fail to explain the observed overfitting. Finally, we study several classical and modern deep learning remedies for overfitting, including regularization and data augmentation, and find that no approach in isolation improves significantly upon the gains achieved by early stopping. All code for reproducing the experiments as well as pretrained model weights and training logs can be found at https://github.com/ locuslab/robust_overfitting.

The combination of inducing point methods with stochastic variational inference has enabled approximate Gaussian Process (GP) inference on large datasets. Unfortunately, the resulting predictive distributions often exhibit substantially underestimated uncertainties. Notably, in the regression case the predictive variance is typically dominated by observation noise, yielding uncertainty estimates that make little use of the input-dependent function uncertainty that makes GP priors attractive. In this work we propose two simple methods for scalable GP regression that address this issue and thus yield substantially improved predictive uncertainties. The first applies variational inference to FITC (Fully Independent Training Conditional; Snelson et. al. 2006). The second bypasses posterior approximations and instead directly targets the posterior predictive distribution. In an extensive empirical comparison with a number of alternative methods for scalable GP regression, we find that the resulting predictive distributions exhibit significantly better calibrated uncertainties and higher log likelihoods--often by as much as half a nat per datapoint.

Reinforcement learning with function approximation can be unstable and even divergent, especially when combined with off-policy learning and Bellman updates. In deep reinforcement learning, these issues have been dealt with empirically by adapting and regularizing the representation, in particular with auxiliary tasks. This suggests that representation learning may provide a means to guarantee stability. In this paper, we formally show that there are indeed nontrivial state representations under which the canonical SARSA algorithm is stable, even when learning off-policy. We analyze representation learning schemes that are based on the transition matrix of a policy, such as proto-value functions, along three axes: approximation error, stability, and ease of estimation. In the most general case of a defective transition matrix, we show that a Schur basis provides convergence guarantees, but is difficult to estimate from samples. For a fixed reward function, we find that an orthogonal basis of the corresponding Krylov subspace is an even better choice. We conclude by empirically demonstrating that these stable representations can be learned using stochastic gradient descent, opening the door to improved techniques for representation learning with deep networks.

Given n values possessed by n agents, we study the problem of estimating the mean by truthfully eliciting agents' answers to multiple-choice questions about their values. We consider two natural candidates for estimation error: mean squared error (MSE) and mean absolute error (MAE). We design a randomized estimator which is asymptotically optimal for both measures in the worst case. In the case where prior distributions over the agents' values are known, we give an optimal, polynomial-time algorithm for MSE, and show that the task of computing an optimal estimate for MAE is #P-hard. Finally, we demonstrate empirically that knowledge of prior distributions gives a significant edge.

Neural networks and tree ensembles are state-of-the-art learners, each with its unique statistical and computational advantages. We aim to combine these advantages by introducing a new layer for neural networks, composed of an ensemble of differentiable decision trees (a.k.a. soft trees). While differentiable trees demonstrate promising results in the literature, they are typically slow in training and inference as they do not support conditional computation. We mitigate this issue by introducing a new sparse activation function for sample routing, and implement true conditional computation by developing specialized forward and backward propagation algorithms that exploit sparsity. Our efficient algorithms pave the way for jointly training over deep and wide tree ensembles using first-order methods (e.g., SGD). Experiments on 23 classification datasets indicate over 10x speed-ups compared to the differentiable trees used in the literature and over 20x reduction in the number of parameters compared to gradient boosted trees, while maintaining competitive performance. Moreover, experiments on CIFAR, MNIST, and Fashion MNIST indicate that replacing dense layers in CNNs with our tree layer reduces the test loss by 7-53% and the number of parameters by 8x. We provide an open-source TensorFlow implementation with a Keras API.

Current transfer learning methods are mainly based on finetuning a pretrained model with target-domain data. Motivated by the techniques from adversarial machine learning (ML) that are capable of manipulating the model prediction via data perturbations, in this paper we propose a novel approach, black-box adversarial reprogramming (BAR), that repurposes a well-trained black-box ML model (e.g., a prediction API or a proprietary software) for solving different ML tasks, especially in the scenario with scarce data and constrained resources. The rationale lies in exploiting high-performance but unknown ML models to gain learning capability for transfer learning. Using zeroth order optimization and multi-label mapping techniques, BAR can reprogram a black-box ML model solely based on its input-output responses without knowing the model architecture or changing any parameter. More importantly, in the limited medical data setting, on autism spectrum disorder classification, diabetic retinopathy detection, and melanoma detection tasks, BAR outperforms state-of-the-art methods and yields comparable performance to the vanilla adversarial reprogramming method requiring complete knowledge of the target ML model. BAR also outperforms baseline transfer learning approaches by a significant margin, demonstrating cost-effective means and new insights for transfer learning.

Over-parameterization is ubiquitous nowadays in training neural networks to benefit both optimization in seeking global optima and generalization in reducing prediction error. However, compressive networks are desired in many real world ap- plications and direct training of small networks may be trapped in local optima. In this paper, in- stead of pruning or distilling over-parameterized models to compressive ones, we propose a new approach based on differential inclusions of in- verse scale spaces. Specifically, it generates a family of models from simple to complex ones that couples a pair of parameters to simultaneously train over-parameterized deep models and structural sparsity on weights of fully connected and convolutional layers. Such a differential inclusion scheme has a simple discretization, pro- posed as Deep structurally splitting Linearized Bregman Iteration (DessiLBI), whose global convergence analysis in deep learning is established that from any initializations, algorithmic iterations converge to a critical point of empirical risks. Experimental evidence shows that DessiLBI achieve comparable and even better performance than the competitive optimizers in exploring the structural sparsity of several widely used backbones on the benchmark datasets. Remarkably, with early stopping, DessiLBI unveils “winning tickets” in early epochs: the effective sparse structure with comparable test accuracy to fully trained over- parameterized models.

In weakly supervised learning, unbiased risk estimator(URE) is a powerful tool for training classifiers when training and test data are drawn from different distributions. Nevertheless, UREs lead to overfitting in many problem settings when the models are complex like deep networks. In this paper, we investigate reasons for such overfitting by studying a weakly supervised problem called learning with complementary labels. We argue the quality of gradient estimation matters more in risk minimization. Theoretically, we show that a URE gives an unbiased gradient estimator(UGE). Practically, however, UGEs may suffer from huge variance, which causes empirical gradients to be usually far away from true gradients during minimization. To this end, we propose a novel surrogate complementary loss(SCL) framework that trades zero bias with reduced variance and makes empirical gradients more aligned with true gradients in the direction. Thanks to this characteristic, SCL successfully mitigates the overfitting issue and improves URE-based methods.