A Relational Markov Decision Process (RMDP) is a first-order representation to express all instances of a single probabilistic planning domain with possibly unbounded number of objects. Early work in RMDPs outputs generalized (instance-independent) first-order policies or value functions as a means to solve all instances of a domain at once. Unfortunately, this line of work met with limited success due to inherent limitations of the representation space used in such policies or value functions. Can neural models provide the missing link by easily representing more complex generalized policies, thus making them effective on all instances of a given domain?

We present SymNet, the first neural approach for solving RMDPs that are expressed in the probabilistic planning language of RDDL. SymNet trains a set of shared parameters for an RDDL domain using training instances from that domain. For each instance, SymNet first converts it to an instance graph and then uses relational neural models to compute node embeddings. It then scores each ground action as a function over the first-order action symbols and node embeddings related to the action. Given a new test instance from the same domain, SymNet architecture with pre-trained parameters scores each ground action and chooses the best action. This can be accomplished in a single forward pass without any retraining on the test instance, thus implicitly representing a neural generalized policy for the whole domain. Our experiments on nine RDDL domains from IPPC demonstrate that SymNet policies are significantly better than random and sometimes even more effective than training a state-of-the-art deep reactive policy from scratch.

The latent spaces of GAN models often have semantically meaningful directions. Moving in these directions corresponds to human-interpretable image transformations, such as zooming or recoloring, enabling a more controllable generation process. However, the discovery of such directions is currently performed in a supervised manner, requiring human labels, pretrained models, or some form of self-supervision. These requirements severely restrict a range of directions existing approaches can discover. In this paper, we introduce an unsupervised method to identify interpretable directions in the latent space of a pretrained GAN model. By a simple model-agnostic procedure, we find directions corresponding to sensible semantic manipulations without any form of (self-)supervision. Furthermore, we reveal several non-trivial findings, which would be difficult to obtain by existing methods, e.g., a direction corresponding to background removal. As an immediate practical benefit of our work, we show how to exploit this finding to achieve competitive performance for weakly-supervised saliency detection. The implementation of our method is available online.

Planning in Partially Observable Markov Decision Processes (POMDPs) inherently gathers the information necessary to act optimally under uncertainties. The framework can be extended to model pure information gathering tasks by considering belief-based rewards. This allows us to use reward shaping to guide POMDP planning to informative beliefs by using a weighted combination of the original reward and the expected information gain as the objective. In this work we propose a novel online algorithm, Information Particle Filter Tree (IPFT), to solve problems with belief-dependent rewards on continuous domains. It simulates particle-based belief trajectories in a Monte Carlo Tree Search (MCTS) approach to construct a search tree in the belief space. The evaluation shows that the consideration of information gain greatly improves the performance in problems where information gathering is an essential part of the optimal policy.

Sparsity in Deep Neural Networks (DNNs) is studied extensively with the focus of maximizing prediction accuracy given an overall parameter budget. Existing methods rely on uniform or heuristic non-uniform sparsity budgets which have sub-optimal layer-wise parameter allocation resulting in a) lower prediction accuracy or b) higher inference cost (FLOPs). This work proposes Soft Threshold Reparameterization (STR), a novel use of the soft-threshold operator on DNN weights. STR smoothly induces sparsity while learning pruning thresholds thereby obtaining a non-uniform sparsity budget. Our method achieves state-of-the-art accuracy for unstructured sparsity in CNNs (ResNet50 and MobileNetV1 on ImageNet-1K), and, additionally, learns non-uniform budgets that empirically reduce the FLOPs by up to 50%. Notably, STR boosts the accuracy over existing results by up to 10% in the ultra sparse (99%) regime and can also be used to induce low-rank (structured sparsity) in RNNs. In short, STR is a simple mechanism which learns effective sparsity budgets that contrast with popular heuristics. Code, pretrained models and sparsity budgets are at https://github.com/RAIVNLab/STR.

A well-known first-order method for sampling from log-concave probability distributions is the Unadjusted Langevin Algorithm (ULA). This work proposes a new annealing step-size schedule for ULA, which allows to prove new convergence guarantees for sampling from a smooth log-concave distribution, which are not covered by existing state-of-the-art convergence guarantees. To establish this result, we derive a new theoretical bound that relates the Wasserstein distance to total variation distance between any two log-concave distributions that complements the reach of Talagrand $T_2$ inequality. Moreover, applying this new step size schedule to an existing constrained sampling algorithm, we show state-of-the-art convergence rates for sampling from a constrained log-concave distribution, as well as improved dimension dependence.

Motivated by applications to online advertising and recommender systems, we consider a game-theoretic model with delayed rewards and asynchronous, payoff-based feedback. In contrast to previous work on delayed multi-armed bandits, we focus on games with continuous action spaces, and we examine the long-run behavior of strategic agents that follow a no-regret learning policy (but are otherwise oblivious to the game being played, the objectives of their opponents, etc.). To account for the lack of a consistent stream of information (for instance, rewards can arrive out of order and with an a priori unbounded delay), we introduce a gradient-free learning policy where payoff information is placed in a priority queue as it arrives. Somewhat surprisingly, we find that under a standard diagonal concavity assumption, the induced sequence of play converges to Nash Equilibrium (NE) with probability 1, even if the delay between choosing an action and receiving the corresponding reward is unbounded.

Robust perception relies on both bottom-up and top-down signals. Bottom-up signals consist of what's directly observed through sensation. Top-down signals consist of beliefs and expectations based on past experience and the current reportable short-term memory, such as how the phrase `peanut butter and ...' will be completed. The optimal combination of bottom-up and top-down information remains an open question, but the manner of combination must be dynamic and both context and task dependent. To effectively utilize the wealth of potential top-down information available, and to prevent the cacophony of intermixed signals in a bidirectional architecture, mechanisms are needed to restrict information flow. We explore deep recurrent neural net architectures in which bottom-up and top-down signals are dynamically combined using attention. Modularity of the architecture further restricts the sharing and communication of information. Together, attention and modularity direct information flow, which leads to reliable performance improvements in perceptual and language tasks, and in particular improves robustness to distractions and noisy data. We demonstrate on a variety of benchmarks in language modeling, sequential image classification, video prediction and reinforcement learning that the \emph{bidirectional} information flow can improve results over strong baselines.

Stochastic neural networks with discrete random variables are an important class of models for their expressiveness and interpretability. Since direct differentiation and backpropagation is not possible, Monte Carlo gradient estimation techniques are a popular alternative. Efficient stochastic gradient estimators, such Straight-Through and Gumbel-Softmax, work well for shallow stochastic models. Their performance, however, suffers with hierarchical, more complex models.

We focus on hierarchical stochastic networks with multiple layers of Boolean latent variables. To analyze such networks, we introduce the framework of harmonic analysis for Boolean functions to derive an analytic formulation for the bias and variance in the Straight-Through estimator. Exploiting these formulations, we propose \emph{FouST}, a low-bias and low-variance gradient estimation algorithm that is just as efficient. Extensive experiments show that FouST performs favorably compared to state-of-the-art biased estimators and is much faster than unbiased ones.

We investigate the connections between neural networks and simple building blocks in kernel space. In particular, using well established feature space tools such as direct sum, averaging, and moment lifting, we present an algebra for creating “compositional” kernels from bags of features. We show that these operations correspond to many of the building blocks of “neural tangent kernels (NTK)”. Experimentally, we show that there is a correlation in test error between neural network architectures and the associated kernels. We construct a simple neural network architecture using only 3x3 convolutions, 2x2 average pooling, ReLU, and optimized with SGD and MSE loss that achieves 96% accuracy on CIFAR10, and whose corresponding compositional kernel achieves 90% accuracy. We also use our constructions to investigate the relative performance of neural networks, NTKs, and compositional kernels in the small dataset regime. In particular, we find that compositional kernels outperform NTKs and neural networks outperform both kernel methods.

The standard normalization method for neural network (NN) models used in Natural Language Processing (NLP) is layer normalization (LN).This is different than batch normalization (BN), which is widely-adopted in Computer Vision. The preferred use of LN in NLP is principally due to the empirical observation that a (naive/vanilla) use of BN leads to significant performance degradation for NLP tasks; however, a thorough understanding of the underlying reasons for this is not always evident. In this paper, we perform a systematic study of NLP transformer models to understand why BN has a poor performance, as compared to LN. We find that the statistics of NLP data across the batch dimension exhibit large fluctuations throughout training. This results in instability, if BN is naively implemented. To address this, we propose Power Normalization (PN), a novel normalization scheme that resolves this issue by (i) relaxing zero-mean normalization in BN, (ii) incorporating a running quadratic mean instead of per batch statistics to stabilize fluctuations, and (iii) using an approximate backpropagation for incorporating the running statistics in the forward pass. We show theoretically, under mild assumptions, that PN leads to a smaller Lipschitz constant for the loss, compared with BN. Furthermore, we prove that the approximate backpropagation scheme leads to bounded gradients. We extensively test PN for transformers on a range of NLP tasks, and we show that it significantly outperforms both LN and BN. In particular, PN outperforms LN by 0.4/0.6 BLEU on IWSLT14/WMT14 and 5.6/3.0 PPL on PTB/WikiText-103. We make our code publicly available at https://github.com/sIncerass/powernorm.

We introduce a randomly extrapolated primal-dual coordinate descent method that adapts to sparsity of the data matrix and the favorable structures of the objective function. Our method updates only a subset of primal and dual variables with sparse data, and it uses large step sizes with dense data, retaining the benefits of the specific methods designed for each case. In addition to adapting to sparsity, our method attains fast convergence guarantees in favorable cases \textit{without any modifications}. In particular, we prove linear convergence under metric subregularity, which applies to strongly convex-strongly concave problems, linear programs and piecewise linear quadratic functions. We show almost sure convergence of the sequence and optimal sublinear convergence rates for the primal-dual gap and objective values, in the general convex-concave case. Numerical evidence demonstrates the state-of-the-art empirical performance of our method in sparse and dense settings, matching and improving the existing methods.

We study preconditioned gradient-based optimization methods where the preconditioning matrix has block-diagonal form. Such a structural constraint comes with the advantage that the update computation can be parallelized across multiple independent tasks. Our main contribution is to demonstrate that the convergence of these methods can significantly be improved by a randomization technique which corresponds to repartitioning coordinates across tasks during the optimization procedure. We provide a theoretical analysis that accurately characterizes the expected convergence gains of repartitioning and validate our findings empirically on various traditional machine learning tasks. From an implementation perspective, block-separable models are well suited for parallelization and, when shared memory is available, randomization can be implemented on top of existing methods very efficiently to improve convergence.

In display advertising, a small group of sellers and bidders face each other in up to 10^{12} auctions a day. In this context, revenue maximisation via monopoly price learning is a high-value problem for sellers. By nature, these auctions are online and produce a very high frequency stream of data. This results in a computational strain that requires algorithms be real-time. Unfortunately, existing methods, inherited from the batch setting, suffer O(\sqrt(t)) time/memory complexity at each update, prohibiting their use. In this paper, we provide the first algorithm for online learning of monopoly prices in online auctions whose update is constant in time and memory.

We demonstrate two new important properties of the 1-path-norm of shallow neural networks. First, despite its non-smoothness and non-convexity it allows a closed form proximal operator which can be efficiently computed, allowing the use of stochastic proximal-gradient-type methods for regularized empirical risk minimization. Second, when the activation functions is differentiable, it provides an upper bound on the Lipschitz constant of the network. Such bound is tighter than the trivial layer-wise product of Lipschitz constants, motivating its use for training networks robust to adversarial perturbations. In practical experiments we illustrate the advantages of using the proximal mapping and we compare the robustness-accuracy trade-off induced by the 1-path-norm, L1-norm and layer-wise constraints on the Lipschitz constant (Parseval networks).

Training multiple tasks jointly in one deep network yields reduced latency during inference and better performance over the single-task counterpart by sharing certain layers of a network. However, over-sharing a network could erroneously enforce over-generalization, causing negative knowledge transfer across tasks. Prior works rely on human intuition or pre-computed task relatedness scores for ad hoc branching structures. They provide sub-optimal end results and often require huge efforts for the trial-and-error process.

In this work, we present an automated multi-task learning algorithm that learns where to share or branch within a network, designing an effective network topology that is directly optimized for multiple objectives across tasks. Specifically, we propose a novel tree-structured design space that casts a tree branching operation as a gumbel-softmax sampling procedure. This enables differentiable network splitting that is end-to-end trainable. We validate the proposed method on controlled synthetic data, CelebA, and Taskonomy.

We investigate the use of a non-parametric independence measure, the Hilbert-Schmidt Independence Criterion (HSIC), as a loss-function for learning robust regression and classification models. This loss-function encourages learning models where the distribution of the residuals between the label and the model prediction is statistically independent of the distribution of the instances themselves. This loss-function was first proposed by \citet{mooij2009regression} in the context of learning causal graphs. We adapt it to the task of learning for unsupervised covariate shift: learning on a source domain without access to any instances or labels from the unknown target domain, but with the assumption that $p(y|x)$ (the conditional probability of labels given instances) remains the same in the target domain. We show that the proposed loss is expected to give rise to models that generalize well on a class of target domains characterised by the complexity of their description within a reproducing kernel Hilbert space. Experiments on unsupervised covariate shift tasks demonstrate that models learned with the proposed loss-function outperform models learned with standard loss functions, achieving state-of-the-art results on a challenging cell-microscopy unsupervised covariate shift task.

This paper introduces the boomerang sampler as a novel class of continuous-time non-reversible Markov chain Monte Carlo algorithms. The methodology begins by representing the target density as a density, $e^{-U}$, with respect to a prescribed (usually) Gaussian measure and constructs a continuous trajectory consisting of a piecewise circular path. The method moves from one circular orbit to another according to a rate function which can be written in terms of $U$. We demonstrate that the method is easy to implement and demonstrate empirically that it can out-perform existing benchmark piecewise deterministic Markov processes such as the bouncy particle sampler and the Zig-Zag. In the Bayesian statistics context, these competitor algorithms are of substantial interest in the large data context due to the fact that they can adopt data subsampling techniques which are exact (ie induce no error in the stationary distribution). We demonstrate theoretically and empirically that we can also construct a control-variate subsampling boomerang sampler which is also exact, and which possesses remarkable scaling properties in the large data limit. We furthermore illustrate a factorised version on the simulation of diffusion bridges.

In this paper we introduce a new approach to topic modelling that scales to large datasets by using a compact representation of the data and by leveraging the GPU architecture.
In this approach, topics are learned directly from the
co-occurrence data of the corpus. In particular, we introduce a novel mixture model which we term the Full Dependence Mixture (FDM) model. FDMs model second moment under general generative assumptions on the data. While there is previous work on topic modeling using second moments, we develop a direct stochastic optimization procedure for fitting an FDM with a single Kullback Leibler objective. Moment methods in general have the benefit that an iteration no longer needs to scale with the size of the corpus. Our approach allows us to leverage standard optimizers and GPUs for the problem of topic modeling. In particular, we evaluate the approach on two large datasets, NeurIPS papers and a Twitter corpus, with a large number of topics, and show that the approach performs comparably or better than the standard benchmarks.