ICML 2023 Papers

A distribution shift can have fundamental consequences such as signaling a change in the operating environment or significantly reducing the accuracy of downstream models. Thus, understanding distribution shifts is critical for examining and hopefully mitigating the effect of such a shift. Most prior work has focused on merely detecting if a shift has occurred and assumes any detected shift can be understood and handled appropriately by a human operator. We hope to aid in these manual mitigation tasks by explaining the distribution shift using interpretable transportation maps from the original distribution to the shifted one. We derive our interpretable mappings from a relaxation of the optimal transport problem, where the candidate mappings are restricted to a set of interpretable mappings. We then use a wide array of quintessential examples of distribution shift in real-world tabular, text, and image cases to showcase how our explanatory mappings provide a better balance between detail and interpretability than baseline explanations by both visual inspection and our PercentExplained metric.

We develop an analytical framework to characterize the set of optimal ReLU neural networks by reformulating the non-convex training problem as a convex program. We show that the global optima of the convex parameterization are given by a polyhedral set and then extend this characterization to the optimal set of the non-convex training objective. Since all stationary points of the ReLU training problem can be represented as optima of sub-sampled convex programs, our work provide a general expression for all critical points of the non-convex objective. We then leverage our results to provide an optimal pruning algorithm for computing minimal networks, establish conditions for the regularization path of ReLU networks to be continuous, and develop sensitivity results for minimal ReLU networks.

Data used for analytics and machine learning often take the form of tables with categorical entries. We introduce a family of lossless compression algorithms for such data that proceed in four steps: (i) Estimate latent variables associated to rows and columns; (ii) Partition the table in blocks according to the row/column latents; (iii) Apply a sequential (e.g. Lempel-Ziv) coder to each of the blocks; (iv) Append a compressed encoding of the latents. We evaluate this approach on several benchmark datasets, and study optimal compression in a probabilistic model for tabular data, whereby latent values are independent and table entries are conditionally independent given the latent values. We prove that the model has a well defined entropy rate and satisfies an asymptotic equipartition property. We also prove that classical compression schemes such as Lempel-Ziv and finite-state encoders do not achieve this rate. On the other hand, the latent estimation strategy outlined above achieves the optimal rate.

Super-resolution (SR) techniques designed for real-world applications commonly encounter two primary challenges: generalization performance and restoration accuracy. We demonstrate that when methods are trained using complex, large-range degradations to enhance generalization, a decline in accuracy is inevitable. However, since the degradation in a certain real-world applications typically exhibits a limited variation range, it becomes feasible to strike a trade-off between generalization performance and testing accuracy within this scope. In this work, we introduce a novel approach to craft training degradation distributions using a small set of reference images. Our strategy is founded upon the binned representation of the degradation space and the Frechet distance between degradation distributions. Our results indicate that the proposed technique significantly improves the performance of test images while preserving generalization capabilities in real-world applications.

Policy optimization methods are powerful algorithms in Reinforcement Learning (RL) for their flexibility to deal with policy parameterization and ability to handle model misspecification. However, these methods usually suffer from slow convergence rates and poor sample complexity. Hence it is important to design provably sample efficient algorithms for policy optimization. Yet, recent advances for this problems have only been successful in tabular and linear setting, whose benign structures cannot be generalized to non-linearly parameterized policies. In this paper, we address this problem by leveraging recent advances in value-based algorithms, including bounded eluder-dimension and online sensitivity sampling, to design a low-switching sample-efficient policy optimization algorithm, *LPO*, with general non-linear function approximation. We show that, our algorithm obtains an $\varepsilon$-optimal policy with only $\widetilde{O}(\frac{\text{poly}(d)}{\varepsilon^3})$ samples, where $\varepsilon$ is the suboptimality gap and $d$ is a complexity measure of the function class approximating the policy. This drastically improves previously best-known sample bound for policy optimization algorithms, $\widetilde{O}(\frac{\text{poly}(d)}{\varepsilon^8})$. Moreover, we empirically test our theory with deep neural nets to show the benefits of the theoretical inspiration.

Sparse coding, which refers to modeling a signal as sparse linear combinations of the elements of a learned dictionary, has proven to be a successful (and interpretable) approach in applications such as signal processing, computer vision, and medical imaging. While this success has spurred much work on provable guarantees for dictionary recovery when the learned dictionary is the same size as the ground-truth dictionary, work on the setting where the learned dictionary is larger (or $\textit{over-realized}$) with respect to the ground truth is comparatively nascent. Existing theoretical results in this setting have been constrained to the case of noise-less data. We show in this work that, in the presence of noise, minimizing the standard dictionary learning objective can fail to recover the elements of the ground-truth dictionary in the over-realized regime, regardless of the magnitude of the signal in the data-generating process. Furthermore, drawing from the growing body of work on self-supervised learning, we propose a novel masking objective for which recovering the ground-truth dictionary is in fact optimal as the signal increases for a large class of data-generating processes. We corroborate our theoretical results with experiments across several parameter regimes showing that our proposed objective also enjoys better empirical performance than the standard reconstruction objective.

Mixup is a data augmentation technique that relies on training using random convex combinations of data points and their labels. In recent years, Mixup has become a standard primitive used in the training of state-of-the-art image classification models due to its demonstrated benefits over empirical risk minimization with regards to generalization and robustness. In this work, we try to explain some of this success from a feature learning perspective. We focus our attention on classification problems in which each class may have multiple associated features (or $\textit{views}$) that can be used to predict the class correctly. Our main theoretical results demonstrate that, for a non-trivial class of data distributions with two features per class, training a 2-layer convolutional network using empirical risk minimization can lead to learning only one feature for almost all classes while training with a specific instantiation of Mixup succeeds in learning both features for every class. We also show empirically that these theoretical insights extend to the practical settings of image benchmarks modified to have multiple features.

We study reinforcement learning with function approximation for large-scale Partially Observable Markov Decision Processes (POMDPs) where the state space and observation space are large or even continuous. Particularly, we consider Hilbert space embeddings of POMDP where the feature of latent states and the feature of observations admit a conditional Hilbert space embedding of the observation emission process, and the latent state transition is deterministic. Under the function approximation setup where the optimal latent state-action $Q$-function is linear in the state feature, and the optimal $Q$-function has a gap in actions, we provide a computationally and statistically efficient algorithm for finding the exact optimal policy. We show our algorithm's computational and statistical complexities scale polynomially with respect to the horizon and the intrinsic dimension of the feature on the observation space. Furthermore, we show both the deterministic latent transitions and gap assumptions are necessary to avoid statistical complexity exponential in horizon or dimension. Since our guarantee does not have an explicit dependence on the size of the state and observation spaces, our algorithm provably scales to large-scale POMDPs.

Graph Neural Networks (GNNs) have shown exceptional performance in the task of link prediction. Despite their effectiveness, the high latency brought by non-trivial neighborhood data dependency limits GNNs in practical deployments. Conversely, the known efficient MLPs are much less effective than GNNs due to the lack of relational knowledge. In this work, to combine the advantages of GNNs and MLPs, we start with exploring direct knowledge distillation (KD) methods for link prediction, i.e., predicted logit-based matching and node representation-based matching. Upon observing direct KD analogs do not perform well for link prediction, we propose a relational KD framework, Linkless Link Prediction (LLP), to distill knowledge for link prediction with MLPs. Unlike simple KD methods that match independent link logits or node representations, LLP distills relational knowledge that is centered around each (anchor) node to the student MLP. Specifically, we propose rank-based matching and distribution-based matching strategies that complement each other. Extensive experiments demonstrate that LLP boosts the link prediction performance of MLPs with significant margins and even outperforms the teacher GNNs on 7 out of 8 benchmarks. LLP also achieves a 70.68x speedup in link prediction inference compared to GNNs on the large-scale OGB dataset.

Recent studies have experimentally shown that we can achieve in non-Euclidean metric space effective and efficient graph embedding, which aims to obtain the vertices' representations reflecting the graph's structure in the metric space. Specifically, graph embedding in hyperbolic space has experimentally succeeded in embedding graphs with hierarchical-tree structure, e.g., data in natural languages, social networks, and knowledge bases. However, recent theoretical analyses have shown a much higher upper bound on non-Euclidean graph embedding's generalization error than Euclidean one's, where a high generalization error indicates that the incompleteness and noise in the data can significantly damage learning performance. It implies that the existing bound cannot guarantee the success of graph embedding in non-Euclidean metric space in a practical training data size, which can prevent non-Euclidean graph embedding's application in real problems. This paper provides a novel upper bound of graph embedding's generalization error by evaluating the local Rademacher complexity of the model as a function set of the distances of representation couples. Our bound clarifies that the performance of graph embedding in non-Euclidean metric space, including hyperbolic space, is better than the existing upper bounds suggest. Specifically, our new upper bound is polynomial in the metric space's geometric radius $R$ and can be $O(\frac{1}{S})$ at the fastest, where $S$ is the training data size. Our bound is significantly tighter and faster than the existing one, which can be exponential to $R$ and $O(\frac{1}{\sqrt{S}})$ at the fastest. Specific calculations on example cases show that graph embedding in non-Euclidean metric space can outperform that in Euclidean space with much smaller training data than the existing bound has suggested.

Recently, the study of linear misspecified bandits has generated intriguing implications of the hardness of learning in bandits and reinforcement learning (RL). In particular, Du et al. (2020) shows that even if a learner is given linear features in $\mathbb{R}^d$ that approximate the rewards in a bandit or RL with a uniform error of $\varepsilon$, searching for an $O(\varepsilon)$-optimal action requires pulling at least $\Omega(\exp(d))$ queries. Furthermore, Lattimore et al. (2020) show that a degraded $O(\varepsilon\sqrt{d})$-optimal solution can be learned within $\operatorname{poly}(d/\varepsilon)$ queries. Yet it is unknown whether a structural assumption on the ground-truth parameter, such as sparsity, could break $\varepsilon\sqrt{d}$ barrier. In this paper, we address this question by showing that algorithms can obtain $O(\varepsilon)$-optimal actions by querying $\tilde{O}(\exp(m\varepsilon))$ actions, where $m$ is the sparsity parameter, removing the $\exp(d)$-dependence. We further show (with an information-theoretical lower bound) that this is the best possible if one demands an error $ m^{\delta}\varepsilon$ for $0<\delta<1$. We further show that $\operatorname{poly}(m/\varepsilon)$ bounds are possible when the linear features are "good''. These results provide a nearly complete picture of how sparsity can help in misspecified bandit learning and provide a deeper understanding of when linear features are ``useful'' for bandit and reinforcement learning with misspecification.

In this paper, we present a model-based offline reinforcement learning method that integrates count-based conservatism, named $\texttt{Count-MORL}$. Our method utilizes the count estimates of state-action pairs to quantify model estimation error, marking the first algorithm of demonstrating the efficacy of count-based conservatism in model-based offline deep RL to the best of our knowledge. For our proposed method, we first show that the estimation error is inversely proportional to the frequency of state-action pairs. Secondly, we demonstrate that the learned policy under the count-based conservative model offers near-optimality performance guarantees. Through extensive numerical experiments, we validate that $\texttt{Count-MORL}$ with hash code implementation significantly outperforms existing offline RL algorithms on the D4RL benchmark datasets. The code is accessible at https://github.com/oh-lab/Count-MORL.

A fundamental issue in machine learning is the robustness of the model with respect to changes in the input. In natural language processing, models typically contain a first embedding layer, transforming a sequence of tokens into vector representations. While the robustness with respect to changes of continuous inputs is well-understood, the situation is less clear when considering discrete changes, for instance replacing a word by another in an input sentence. Our work formally proves that popular embedding schemes, such as concatenation, TF-IDF, and Paragraph Vector (a.k.a. doc2vec), exhibit robustness in the Hölder or Lipschitz sense with respect to the Hamming distance. We provide quantitative bounds for these schemes and demonstrate how the constants involved are affected by the length of the document. These findings are exemplified through a series of numerical examples.

We address multi-agent best arm identification with privacy guarantees. In this setting, agents collaborate by communicating to find the optimal arm. To avoid leaking sensitive data through messages, we consider two notions of privacy withholding different kinds of information: differential privacy and $(\epsilon, \eta)$-privacy. For each privacy definition, we propose an algorithm based on a two-level successive elimination scheme. We provide theoretical guarantees for the privacy level, accuracy and sample complexity of our algorithms. Experiments on various settings support our theoretical findings.

Deep graph clustering, which aims to group the nodes of a graph into disjoint clusters with deep neural networks, has achieved promising progress in recent years. However, the existing methods fail to scale to the large graph with million nodes. To solve this problem, a scalable deep graph clustering method (Dink-Net) is proposed with the idea of dilation and shrink. Firstly, by discriminating nodes, whether being corrupted by augmentations, representations are learned in a self-supervised manner. Meanwhile, the cluster centers are initialized as learnable neural parameters. Subsequently, the clustering distribution is optimized by minimizing the proposed cluster dilation loss and cluster shrink loss in an adversarial manner. By these settings, we unify the two-step clustering, i.e., representation learning and clustering optimization, into an end-to-end framework, guiding the network to learn clustering-friendly features. Besides, Dink-Net scales well to large graphs since the designed loss functions adopt the mini-batch data to optimize the clustering distribution even without performance drops. Both experimental results and theoretical analyses demonstrate the superiority of our method. Compared to the runner-up, Dink-Net achieves $9.62\%$ NMI improvement on the ogbn-papers100M dataset with 111 million nodes and 1.6 billion edges. The source code is released: https://github.com/yueliu1999/Dink-Net. Besides, a collection (papers, codes, and datasets) of deep graph clustering is shared on GitHub https://github.com/yueliu1999/Awesome-Deep-Graph-Clustering.

Although disentangled representations are often said to be beneficial for downstream tasks, current empirical and theoretical understanding is limited. In this work, we provide evidence that disentangled representations coupled with sparse task-specific predictors improve generalization. In the context of multi-task learning, we prove a new identifiability result that provides conditions under which maximally sparse predictors yield disentangled representations. Motivated by this theoretical result, we propose a practical approach to learn disentangled representations based on a sparsity-promoting bi-level optimization problem. Finally, we explore a meta-learning version of this algorithm based on group Lasso multiclass SVM predictors, for which we derive a tractable dual formulation. It obtains competitive results on standard few-shot classification benchmarks, while each task is using only a fraction of the learned representations.

Meta-learning algorithms are able to learn a new task using previously learned knowledge, but they often require a large number of meta-training tasks which may not be readily available. To address this issue, we propose a method for few-shot learning with fewer tasks, which we call MetaModulation. The key idea is to use a neural network to increase the density of the meta-training tasks by modulating batch normalization parameters during meta-training. Additionally, we modify parameters at various neural network levels, rather than just a single layer, to increase task diversity. To account for the uncertainty caused by the reduced number of training tasks, we propose a variational MetaModulation where the modulation parameters are treated as latent variables. We also introduce learning variational feature hierarchies by the variational MetaModulation, which modulates features at all layers and can take into account task uncertainty and generate more diverse tasks. The ablation studies illustrate the advantages of utilizing a learnable task modulation at different levels and demonstrate the benefit of incorporating probabilistic variants in few-task meta-learning. Our MetaModulation and its variational variants consistently outperform state-of-the-art alternatives on four few-task meta-learning benchmarks.

Adversarial training is well-known to produce high-quality neural network models that are empirically robust against adversarial perturbations. Nevertheless, once a model has been adversarially trained, one often desires a certification that the model is truly robust against all future attacks. Unfortunately, when faced with adversarially trained models, all existing approaches have significant trouble making certifications that are strong enough to be practically useful. Linear programming (LP) techniques in particular face a ``convex relaxation barrier'' that prevent them from making high-quality certifications, even after refinement with mixed-integer linear programming (MILP) and branch-and-bound (BnB) techniques. In this paper, we propose a nonconvex certification technique, based on a low-rank restriction of a semidefinite programming (SDP) relaxation. The nonconvex relaxation makes strong certifications comparable to much more expensive SDP methods, while optimizing over dramatically fewer variables comparable to much weaker LP methods. Despite nonconvexity, we show how off-the-shelf local optimization algorithms can be used to achieve and to certify global optimality in polynomial time. Our experiments find that the nonconvex relaxation almost completely closes the gap towards exact certification of adversarially trained models.

SARSA, a classical on-policy control algorithm for reinforcement learning, is known to chatter when combined with linear function approximation: SARSA does not diverge but oscillates in a bounded region. However, little is known about how fast SARSA converges to that region and how large the region is. In this paper, we make progress towards this open problem by showing the convergence rate of projected SARSA to a bounded region. Importantly, the region is much smaller than the region that we project into, provided that the the magnitude of the reward is not too large. Existing works regarding the convergence of linear SARSA to a fixed point all require the Lipschitz constant of SARSA's policy improvement operator to be sufficiently small; our analysis instead applies to arbitrary Lipschitz constants and thus characterizes the behavior of linear SARSA for a new regime.