ICML 2022 Papers

In this paper, we revisit the regret minimization problem in sparse stochastic contextual linear bandits, where feature vectors may be of large dimension $d$, but where the reward function depends on a few, say $s_0\ll d$, of these features only. We present Thresholded Lasso bandit, an algorithm that (i) estimates the vector defining the reward function as well as its sparse support, i.e., significant feature elements, using the Lasso framework with thresholding, and (ii) selects an arm greedily according to this estimate projected on its support. The algorithm does not require prior knowledge of the sparsity index $s_0$ and can be parameter-free under some symmetric assumptions. For this simple algorithm, we establish non-asymptotic regret upper bounds scaling as $\mathcal{O}( \log d + \sqrt{T} )$ in general, and as $\mathcal{O}( \log d + \log T)$ under the so-called margin condition (a probabilistic condition on the separation of the arm rewards). The regret of previous algorithms scales as $\mathcal{O}( \log d + \sqrt{T \log (d T)})$ and $\mathcal{O}( \log T \log d)$ in the two settings, respectively. Through numerical experiments, we confirm that our algorithm outperforms existing methods.

We justify the fast equilibrium conjecture on stochastic gradient descent from (Li et al. 2020) under the assumptions that critical points are non-degenerate and the stochastic noise is a standard Gaussian. In this case, we prove an SGD with constant effective learning rate consists of three stages: descent, diffusion and tunneling, and explicitly identify temporary equilibrium states in the normalized parameter space that can be observed within practical training time. This interprets the gap between the mixing time in the fast equilibrium conjecture and the previously known upper bound. While our assumptions do not represent typical implementations of SGD of neural networks in practice, this is the first description of the three-stage mechanism in any case. The main finding in this mechanism is that a temporary equilibrium of local nature is quickly achieved after polynomial time (in term of the reciprocal of the intrinsic learning rate) and then stabilizes within observable time scales; and that the temporary equilibrium is in general different from the global Gibbs equilibrium, which will only appear after an exponentially long period beyond typical training limits. Our experiments support that this mechanism may extend to the general case.

We study the problem of online multi-task learning where the tasks are performed within similar but not necessarily identical multi-armed bandit environments. In particular, we study how a learner can improve its overall performance across multiple related tasks through robust transfer of knowledge. While an upper confidence bound (UCB)-based algorithm has recently been shown to achieve nearly-optimal performance guarantees in a setting where all tasks are solved concurrently, it remains unclear whether Thompson sampling (TS) algorithms, which have superior empirical performance in general, share similar theoretical properties. In this work, we present a TS-type algorithm for a more general online multi-task learning protocol, which extends the concurrent setting. We provide its frequentist analysis and prove that it is also nearly-optimal using a novel concentration inequality for multi-task data aggregation at random stopping times. Finally, we evaluate the algorithm on synthetic data and show that the TS-type algorithm enjoys superior empirical performance in comparison with the UCB-based algorithm and a baseline algorithm that performs TS for each individual task without transfer.

Existing methods of combinatorial pure exploration mainly focus on the UCB approach. To make the algorithm efficient, they usually use the sum of upper confidence bounds within arm set $S$ to represent the upper confidence bound of $S$, which can be much larger than the tight upper confidence bound of $S$ and leads to a much higher complexity than necessary, since the empirical means of different arms in $S$ are independent. To deal with this challenge, we explore the idea of Thompson Sampling (TS) that uses independent random samples instead of the upper confidence bounds, and design the first TS-based algorithm TS-Explore for (combinatorial) pure exploration. In TS-Explore, the sum of independent random samples within arm set $S$ will not exceed the tight upper confidence bound of $S$ with high probability. Hence it solves the above challenge, and achieves a lower complexity upper bound than existing efficient UCB-based algorithms in general combinatorial pure exploration. As for pure exploration of classic multi-armed bandit, we show that TS-Explore achieves an asymptotically optimal complexity upper bound.

Gradient-free/zeroth-order methods for black-box convex optimization have been extensively studied in the last decade with the main focus on oracle calls complexity. In this paper, besides the oracle complexity, we focus also on iteration complexity, and propose a generic approach that, based on optimal first-order methods, allows to obtain in a black-box fashion new zeroth-order algorithms for non-smooth convex optimization problems. Our approach not only leads to optimal oracle complexity, but also allows to obtain iteration complexity similar to first-order methods, which, in turn, allows to exploit parallel computations to accelerate the convergence of our algorithms. We also elaborate on extensions for stochastic optimization problems, saddle-point problems, and distributed optimization.

Autoencoders are the simplest neural network for unsupervised learning, and thus an ideal framework for studying feature learning. While a detailed understanding of the dynamics of linear autoencoders has recently been obtained, the study of non-linear autoencoders has been hindered by the technical difficulty of handling training data with non-trivial correlations {–} a fundamental prerequisite for feature extraction. Here, we study the dynamics of feature learning in non-linear, shallow autoencoders. We derive a set of asymptotically exact equations that describe the generalisation dynamics of autoencoders trained with stochastic gradient descent (SGD) in the limit of high-dimensional inputs. These equations reveal that autoencoders learn the leading principal components of their inputs sequentially. An analysis of the long-time dynamics explains the failure of sigmoidal autoencoders to learn with tied weights, and highlights the importance of training the bias in ReLU autoencoders. Building on previous results for linear networks, we analyse a modification of the vanilla SGD algorithm which allows learning of the exact principal components. Finally, we show that our equations accurately describe the generalisation dynamics of non-linear autoencoders on realistic datasets such as CIFAR10.

Recent years have seen the emergence of pre-trained representations as a powerful abstraction for AI applications in computer vision, natural language, and speech. However, policy learning for control is still dominated by a tabula-rasa learning paradigm, with visuo-motor policies often trained from scratch using data from deployment environments. In this context, we revisit and study the role of pre-trained visual representations for control, and in particular representations trained on large-scale computer vision datasets. Through extensive empirical evaluation in diverse control domains (Habitat, DeepMind Control, Adroit, Franka Kitchen), we isolate and study the importance of different representation training methods, data augmentations, and feature hierarchies. Overall, we find that pre-trained visual representations can be competitive or even better than ground-truth state representations to train control policies. This is in spite of using only out-of-domain data from standard vision datasets, without any in-domain data from the deployment environments.

Teaching dimension (TD) is a fundamental theoretical property for understanding machine teaching algorithms. It measures the sample complexity of teaching a target hypothesis to a learner. The TD of linear learners has been studied extensively, whereas the results of teaching non-linear learners are rare. A recent result investigates the TD of polynomial and Gaussian kernel learners. Unfortunately, the theoretical bounds therein show that the TD is high when teaching those non-linear learners. Inspired by the fact that regularization can reduce the learning complexity in machine learning, a natural question is whether the similar fact happens in machine teaching. To answer this essential question, this paper proposes a unified theoretical framework termed STARKE to analyze the TD of regularized kernel learners. On the basis of STARKE, we derive a generic result of any type of kernels. Furthermore, we disclose that the TD of regularized linear and regularized polynomial kernel learners can be strictly reduced. For regularized Gaussian kernel learners, we reveal that, although their TD is infinite, their epsilon-approximate TD can be exponentially reduced compared with that of the unregularized learners. The extensive experimental results of teaching the optimization-based learners verify the theoretical findings.

The use of sparse neural networks has seen rapid growth in recent years, particularly in computer vision. Their appeal stems largely from the reduced number of parameters required to train and store, as well as in an increase in learning efficiency. Somewhat surprisingly, there have been very few efforts exploring their use in Deep Reinforcement Learning (DRL). In this work we perform a systematic investigation into applying a number of existing sparse training techniques on a variety of DRL agents and environments. Our results corroborate the findings from sparse training in the computer vision domain {–}sparse networks perform better than dense networks for the same parameter count{–} in the DRL domain. We provide detailed analyses on how the various components in DRL are affected by the use of sparse networks and conclude by suggesting promising avenues for improving the effectiveness of sparse training methods, as well as for advancing their use in DRL.

Meta-learning has emerged as a potent paradigm for quick learning of few-shot tasks, by leveraging the meta-knowledge learned from meta-training tasks. Well-generalized meta-knowledge that facilitates fast adaptation in each task is preferred; however, recent evidence suggests the undesirable memorization effect where the meta-knowledge simply memorizing all meta-training tasks discourages task-specific adaptation and poorly generalizes. There have been several solutions to mitigating the effect, including both regularizer-based and augmentation-based methods, while a systematic understanding of these methods in a single framework is still lacking. In this paper, we offer a novel causal perspective of meta-learning. Through the lens of causality, we conclude the universal label space as a confounder to be the causing factor of memorization and frame the two lines of prevailing methods as different deconfounder approaches. Remarkably, derived from the causal inference principle of front-door adjustment, we propose two frustratingly easy but effective deconfounder algorithms, i.e., sampling multiple versions of the meta-knowledge via Dropout and grouping the meta-knowledge into multiple bins. The proposed causal perspective not only brings in the two deconfounder algorithms that surpass previous works in four benchmark datasets towards combating memorization, but also opens a promising direction for meta-learning.

This work identifies a common flaw of deep reinforcement learning (RL) algorithms: a tendency to rely on early interactions and ignore useful evidence encountered later. Because of training on progressively growing datasets, deep RL agents incur a risk of overfitting to earlier experiences, negatively affecting the rest of the learning process. Inspired by cognitive science, we refer to this effect as the primacy bias. Through a series of experiments, we dissect the algorithmic aspects of deep RL that exacerbate this bias. We then propose a simple yet generally-applicable mechanism that tackles the primacy bias by periodically resetting a part of the agent. We apply this mechanism to algorithms in both discrete (Atari 100k) and continuous action (DeepMind Control Suite) domains, consistently improving their performance.

Modern reinforcement learning (RL) commonly engages practical problems with large state spaces, where function approximation must be deployed to approximate either the value function or the policy. While recent progresses in RL theory address a rich set of RL problems with general function approximation, such successes are mostly restricted to the single-agent setting. It remains elusive how to extend these results to multi-agent RL, especially in the face of new game-theoretical challenges. This paper considers two-player zero-sum Markov Games (MGs). We propose a new algorithm that can provably find the Nash equilibrium policy using a polynomial number of samples, for any MG with low

We introduce the Poisson Binomial mechanism (PBM), a discrete differential privacy mechanism for distributed mean estimation (DME) with applications to federated learning and analytics. We provide a tight analysis of its privacy guarantees, showing that it achieves the same privacy-accuracy trade-offs as the continuous Gaussian mechanism. Our analysis is based on a novel bound on the Rényi divergence of two Poisson binomial distributions that may be of independent interest. Unlike previous discrete DP schemes based on additive noise, our mechanism encodes local information into a parameter of the binomial distribution, and hence the output distribution is discrete with bounded support. Moreover, the support does not increase as the privacy budget goes to zero as in the case of additive schemes which require the addition of more noise to achieve higher privacy; on the contrary, the support becomes smaller as eps goes to zero. The bounded support enables us to combine our mechanism with secure aggregation (SecAgg), a multi-party cryptographic protocol, without the need of performing modular clipping which results in an unbiased estimator of the sum of the local vectors. This in turn allows us to apply it in the private FL setting and provide an upper bound on the convergence rate of the SGD algorithm. Moreover, since the support of the output distribution becomes smaller as $\varepsilon \ra 0$, the communication cost of our scheme decreases with the privacy constraint $\varepsilon$, outperforming all previous distributed DP schemes based on additive noise in the high privacy or low communication regimes.

Our theoretical understanding of deep learning has not kept pace with its empirical success. While network architecture is known to be critical, we do not yet understand its effect on learned representations and network behavior, or how this architecture should reflect task structure.In this work, we begin to address this gap by introducing the Gated Deep Linear Network framework that schematizes how pathways of information flow impact learning dynamics within an architecture. Crucially, because of the gating, these networks can compute nonlinear functions of their input. We derive an exact reduction and, for certain cases, exact solutions to the dynamics of learning. Our analysis demonstrates that the learning dynamics in structured networks can be conceptualized as a neural race with an implicit bias towards shared representations, which then govern the model’s ability to systematically generalize, multi-task, and transfer. We validate our key insights on naturalistic datasets and with relaxed assumptions. Taken together, our work gives rise to general hypotheses relating neural architecture to learning and provides a mathematical approach towards understanding the design of more complex architectures and the role of modularity and compositionality in solving real-world problems. The code and results are available at https://www.saxelab.org/gated-dln.

The stochastic block model (SBM) is one of the most widely used generative models for network data. Many continuous-time dynamic network models are built upon the same assumption as the SBM: edges or events between all pairs of nodes are conditionally independent given the block or community memberships, which prevents them from reproducing higher-order motifs such as triangles that are commonly observed in real networks. We propose the multivariate community Hawkes (MULCH) model, an extremely flexible community-based model for continuous-time networks that introduces dependence between node pairs using structured multivariate Hawkes processes. We fit the model using a spectral clustering and likelihood-based local refinement procedure. We find that our proposed MULCH model is far more accurate than existing models both for predictive and generative tasks.

The Contextual Graph Markov Model (CGMM) is a deep, unsupervised, and probabilistic model for graphs that is trained incrementally on a layer-by-layer basis. As with most Deep Graph Networks, an inherent limitation is the need to perform an extensive model selection to choose the proper size of each layer’s latent representation. In this paper, we address this problem by introducing the Infinite Contextual Graph Markov Model (iCGMM), the first deep Bayesian nonparametric model for graph learning. During training, iCGMM can adapt the complexity of each layer to better fit the underlying data distribution. On 8 graph classification tasks, we show that iCGMM: i) successfully recovers or improves CGMM’s performances while reducing the hyper-parameters’ search space; ii) performs comparably to most end-to-end supervised methods. The results include studies on the importance of depth, hyper-parameters, and compression of the graph embeddings. We also introduce a novel approximated inference procedure that better deals with larger graph topologies.

In the maximum state entropy exploration framework, an agent interacts with a reward-free environment to learn a policy that maximizes the entropy of the expected state visitations it is inducing. Hazan et al. (2019) noted that the class of Markovian stochastic policies is sufficient for the maximum state entropy objective, and exploiting non-Markovianity is generally considered pointless in this setting. In this paper, we argue that non-Markovianity is instead paramount for maximum state entropy exploration in a finite-sample regime. Especially, we recast the objective to target the expected entropy of the induced state visitations in a single trial. Then, we show that the class of non-Markovian deterministic policies is sufficient for the introduced objective, while Markovian policies suffer non-zero regret in general. However, we prove that the problem of finding an optimal non-Markovian policy is NP-hard. Despite this negative result, we discuss avenues to address the problem in a tractable way and how non-Markovian exploration could benefit the sample efficiency of online reinforcement learning in future works.

The space of value functions is a fundamental concept in reinforcement learning. Characterizing its geometric properties may provide insights for optimization and representation. Existing works mainly focus on the value space for Markov Decision Processes (MDPs). In this paper, we study the geometry of the robust value space for the more general Robust MDPs (RMDPs) setting, where transition uncertainties are considered. Specifically, since we find it hard to directly adapt prior approaches to RMDPs, we start with revisiting the non-robust case, and introduce a new perspective that enables us to characterize both the non-robust and robust value space in a similar fashion. The key of this perspective is to decompose the value space, in a state-wise manner, into unions of hypersurfaces. Through our analysis, we show that the robust value space is determined by a set of conic hypersurfaces, each of which contains the robust values of all policies that agree on one state. Furthermore, we find that taking only extreme points in the uncertainty set is sufficient to determine the robust value space. Finally, we discuss some other aspects about the robust value space, including its non-convexity and policy agreement on multiple states.

We consider the problem of training a $d$ dimensional model with distributed differential privacy (DP) where secure aggregation (SecAgg) is used to ensure that the server only sees the noisy sum of $n$ model updates in every training round. Taking into account the constraints imposed by SecAgg, we characterize the fundamental communication cost required to obtain the best accuracy achievable under $\varepsilon$ central DP (i.e. under a fully trusted server and no communication constraints). Our results show that $\tilde{O}\lp \min(n^2\varepsilon^2, d) \rp$ bits per client are both sufficient and necessary, and this fundamental limit can be achieved by a linear scheme based on sparse random projections. This provides a significant improvement relative to state-of-the-art SecAgg distributed DP schemes which use $\tilde{O}(d\log(d/\varepsilon^2))$ bits per client. Empirically, we evaluate our proposed scheme on real-world federated learning tasks. We find that our theoretical analysis is well matched in practice. In particular, we show that we can reduce the communication cost to under $1.78$ bits per parameter in realistic privacy settings without decreasing test-time performance. Our work hence theoretically and empirically specifies the fundamental price of using SecAgg.