ICML 2023 Papers

Approximate inference in Gaussian process (GP) models with non-conjugate likelihoods gets entangled with the learning of the model hyperparameters. We improve hyperparameter learning in GP models and focus on the interplay between variational inference (VI) and the learning target. While VI's lower bound to the marginal likelihood is a suitable objective for inferring the approximate posterior, we show that a direct approximation of the marginal likelihood as in Expectation Propagation (EP) is a better learning objective for hyperparameter optimization. We design a hybrid training procedure to bring the best of both worlds: it leverages conjugate-computation VI for inference and uses an EP-like marginal likelihood approximation for hyperparameter learning. We compare VI, EP, Laplace approximation, and our proposed training procedure and empirically demonstrate the effectiveness of our proposal across a wide range of data sets.

Based on binary inquiries, we developed an algorithm to estimate population quantiles under Local Differential Privacy (LDP). By self-normalizing, our algorithm provides asymptotically normal estimation with valid inference, resulting in tight confidence intervals without the need for nuisance parameters to be estimated. Our proposed method can be conducted fully online, leading to high computational efficiency and minimal storage requirements with $\mathcal{O}(1)$ space. We also proved an optimality result by an elegant application of one central limit theorem of Gaussian Differential Privacy (GDP) when targeting the frequently encountered median estimation problem. With mathematical proof and extensive numerical testing, we demonstrate the validity of our algorithm both theoretically and experimentally.

Directed acyclic graphs (DAGs) encode a lot of information about a particular distribution in their structure. However, compute required to infer these structures is typically super-exponential in the number of variables, as inference requires a sweep of a combinatorially large space of potential structures. That is, until recent advances made it possible to search this space using a differentiable metric, drastically reducing search time. While this technique--- named NOTEARS ---is widely considered a seminal work in DAG-discovery, it concedes an important property in favour of differentiability: transportability. To be transportable, the structures discovered on one dataset must apply to another dataset from the same domain. We introduce D-Struct which recovers transportability in the discovered structures through a novel architecture and loss function while remaining fully differentiable. Because D-Struct remains differentiable, our method can be easily adopted in existing differentiable architectures, as was previously done with NOTEARS. In our experiments, we empirically validate D-Struct with respect to edge accuracy and structural Hamming distance in a variety of settings.

Contrastively trained encoders have recently been proven to invert the data-generating process: they encode each input, e.g., an image, into the true latent vector that generated the image (Zimmermann et al., 2021). However, real-world observations often have inherent ambiguities. For instance, images may be blurred or only show a 2D view of a 3D object, so multiple latents could have generated them. This makes the true posterior for the latent vector probabilistic with heteroscedastic uncertainty. In this setup, we extend the common InfoNCE objective and encoders to predict latent distributions instead of points. We prove that these distributions recover the correct posteriors of the data-generating process, including its level of aleatoric uncertainty, up to a rotation of the latent space. In addition to providing calibrated uncertainty estimates, these posteriors allow the computation of credible intervals in image retrieval. They comprise images with the same latent as a given query, subject to its uncertainty. Code is at https://github.com/mkirchhof/Probabilistic_Contrastive_Learning .

Graph coarsening is a technique for solving large-scale graph problems by working on a smaller version of the original graph, and possibly interpolating the results back to the original graph. It has a long history in scientific computing and has recently gained popularity in machine learning, particularly in methods that preserve the graph spectrum. This work studies graph coarsening from a different perspective, developing a theory for preserving graph distances and proposing a method to achieve this. The geometric approach is useful when working with a collection of graphs, such as in graph classification and regression. In this study, we consider a graph as an element on a metric space equipped with the Gromov--Wasserstein (GW) distance, and bound the difference between the distance of two graphs and their coarsened versions. Minimizing this difference can be done using the popular weighted kernel $K$-means method, which improves existing spectrum-preserving methods with the proper choice of the kernel. The study includes a set of experiments to support the theory and method, including approximating the GW distance, preserving the graph spectrum, classifying graphs using spectral information, and performing regression using graph convolutional networks. Code is available at https://github.com/ychen-stat-ml/GW-Graph-Coarsening.

Nonconvex optimization is central in solving many machine learning problems, in which block-wise structure is commonly encountered. In this work, we propose cyclic block coordinate methods for nonconvex optimization problems with non-asymptotic gradient norm guarantees. Our convergence analysis is based on a gradient Lipschitz condition with respect to a Mahalanobis norm, inspired by a recent progress on cyclic block coordinate methods. In deterministic settings, our convergence guarantee matches the guarantee of (full-gradient) gradient descent, but with the gradient Lipschitz constant being defined w.r.t. a Mahalanobis norm. In stochastic settings, we use recursive variance reduction to decrease the per-iteration cost and match the arithmetic operation complexity of current optimal stochastic full-gradient methods, with a unified analysis for both finite-sum and infinite-sum cases. We prove a faster linear convergence result when a Polyak-Łojasiewicz (PŁ) condition holds. To our knowledge, this work is the first to provide non-asymptotic convergence guarantees --- variance-reduced or not --- for a cyclic block coordinate method in general composite (smooth + nonsmooth) nonconvex settings. Our experimental results demonstrate the efficacy of the proposed cyclic scheme in training deep neural nets.

We consider the problem of decentralized multi-agent reinforcement learning in Markov games. A fundamental question is whether there exist algorithms that, when run independently by all agents, lead to no-regret for each player, analogous to celebrated convergence results for no-regret learning in normal-form games. While recent work has shown that such algorithms exist for restricted settings (notably, when regret is defined with respect to deviations to Markov policies), the question of whether independent no-regret learning can be achieved in the standard Markov game framework was open. We provide a decisive negative resolution to this problem, both from a computational and statistical perspective. We show that: • Under the complexity-theoretic assumption that PPAD $\neq$ P, there is no polynomial-time algorithm that attains no-regret in two-player general-sum Markov games when executed independently by all players, even when the game is known to the algorithm designer. • When the game is unknown, no algorithm, efficient or otherwise, can achieve no-regret without observing exponentially many episodes in the number of players. These results are proven via lower bounds for a simpler problem we refer to as SparseCCE, in which the goal is to compute a coarse correlated equilibrium that is ``sparse'' in the sense that it can be represented as a mixture of a small number of product policies.

To mitigate the bias exhibited by machine learning models, fairness criteria can be integrated into the training process to ensure fair treatment across all demographics, but it often comes at the expense of model performance. Understanding such tradeoffs, therefore, underlies the design of fair algorithms. To this end, this paper provides a complete characterization of the inherent tradeoff of demographic parity on classification problems, under the most general multi-group, multi-class, and noisy setting. Specifically, we show that the minimum error rate achievable by randomized and attribute-aware fair classifiers is given by the optimal value of a Wasserstein-barycenter problem. On the practical side, our findings lead to a simple post-processing algorithm that derives fair classifiers from score functions, which yields the optimal fair classifier when the score is Bayes optimal. We provide suboptimality analysis and sample complexity for our algorithm, and demonstrate its effectiveness on benchmark datasets.

Long-tailed learning is one of the most challenging problems in visual recognition. There are some studies aiming to solve long-tailed classification from the perspective of feature learning. Recent work proposes to learn the balanced representation by fixing the linear classifier as Equiangular Tight Frame (ETF), since they argue what matters in classification is the structure of the feature, instead of their directions. Holding a different view, in this paper, we show that features with fixed directions may be harmful to the generalization of models, even if it is completely symmetric. To avoid this issue, we propose Representation-Balanced Learning Framework (RBL), which introduces orthogonal matrices to learn directions while maintaining the geometric structure of ETF. Theoretically, our contributions are two-fold: 1). we point out that the feature learning of RBL is insensitive toward training set label distribution, it always learns a balanced representation space. 2). we provide a generalization analysis of proposed RBL through training stability. To analyze the stability of the parameter with orthogonal constraint, we propose a novel training stability analysis paradigm, Two-Parameter Model Stability. Practically, our method is extremely simple in implementation but shows great superiority on several benchmark datasets.

The noise transition matrix plays a central role in the problem of learning with noisy labels. Among many other reasons, a large number of existing solutions rely on the knowledge of it. Identifying and estimating the transition matrix without ground truth labels is a critical and challenging task. When label noise transition depends on each instance, the problem of identifying the instance-dependent noise transition matrix becomes substantially more challenging. Despite recently proposed solutions for learning from instance-dependent noisy labels, the literature lacks a unified understanding of when such a problem remains identifiable. The goal of this paper is to characterize the identifiability of the label noise transition matrix. Building on Kruskal's identifiability results, we are able to show the necessity of multiple noisy labels in identifying the noise transition matrix at the instance level. We further instantiate the results to explain the successes of the state-of-the-art solutions and how additional assumptions alleviated the requirement of multiple noisy labels. Our result reveals that disentangled features improve identification. This discovery led us to an approach that improves the estimation of the transition matrix using properly disentangled features. Code is available at https://github.com/UCSC-REAL/Identifiability.

An unaddressed challenge in multi-agent coordination is to enable AI agents to exploit the semantic relationships between the features of actions and the features of observations. Humans take advantage of these relationships in highly intuitive ways. For instance, in the absence of a shared language, we might point to the object we desire or hold up our fingers to indicate how many objects we want. To address this challenge, we investigate the effect of network architecture on the propensity of learning algorithms to exploit these semantic relationships. Across a procedurally generated coordination task, we find that attention-based architectures that jointly process a featurized representation of observations and actions have a better inductive bias for learning intuitive policies. Through fine-grained evaluation and scenario analysis, we show that the resulting policies are human-interpretable. Moreover, such agents coordinate with people without training on any human data.

Given a reference set R of n points and a query set Q of m points in a metric space, this paper studies an important problem of finding k-nearest neighbors of every point q of Q in the set R in a near-linear time. In the paper at ICML 2006, Beygelzimer, Kakade, and Langford introduced a cover tree and attempted to prove that this tree can be built in O(n log n) time while the nearest neighbor search can be done O(n log m) time with a hidden dimensionality factor. In 2015, section 5.3 of Curtin's PhD pointed out that the proof of the latter claim can have a serious gap in time complexity estimation. A paper at TopoInVis 2022 reported explicit counterexamples for a key step in the proofs of both claims. The past obstacles will be overcome by a simpler compressed cover tree on the reference set R. The first new algorithm constructs a compressed cover tree in O(n log n) time. The second new algorithm finds all k-nearest neighbors of all points from Q using a compressed cover tree in time O(m(k+log n)log k) with a hidden dimensionality factor depending on point distributions of the sets R,Q but not on their sizes.

Off-policy learning from multistep returns is crucial for sample-efficient reinforcement learning, but counteracting off-policy bias without exacerbating variance is challenging. Classically, off-policy bias is corrected in a per-decision manner: past temporal-difference errors are re-weighted by the instantaneous Importance Sampling (IS) ratio after each action via eligibility traces. Many off-policy algorithms rely on this mechanism, along with differing protocols for cutting the IS ratios (traces) to combat the variance of the IS estimator. Unfortunately, once a trace has been cut, the effect cannot be easily reversed. This has led to the development of credit-assignment strategies that account for multiple past experiences at a time. These trajectory-aware methods have not been extensively analyzed, and their theoretical justification remains uncertain. In this paper, we propose a multistep operator that unifies per-decision and trajectory-aware methods. We prove convergence conditions for our operator in the tabular setting, establishing the first guarantees for several existing methods as well as many new ones. Finally, we introduce Recency-Bounded Importance Sampling (RBIS), which leverages trajectory awareness to perform robustly across $\lambda$-values in an off-policy control task.

Natural agents can effectively learn from multiple data sources that differ in size, quality, and types of measurements. We study this heterogeneity in the context of offline reinforcement learning (RL) by introducing a new, practically motivated semi-supervised setting. Here, an agent has access to two sets of trajectories: labelled trajectories containing state, action and reward triplets at every timestep, along with unlabelled trajectories that contain only state and reward information. For this setting, we develop and study a simple meta-algorithmic pipeline that learns an inverse dynamics model on the labelled data to obtain proxy-labels for the unlabelled data, followed by the use of any offline RL algorithm on the true and proxy-labelled trajectories. Empirically, we find this simple pipeline to be highly successful --- on several D4RL benchmarks (Fu et al., 2020), certain offline RL algorithms can match the performance of variants trained on a fully labelled dataset even when we label only 10% of trajectories which are highly suboptimal. To strengthen our understanding, we perform a large-scale controlled empirical study investigating the interplay of data-centric properties of the labelled and unlabelled datasets, with algorithmic design choices (e.g., choice of inverse dynamics, offline RL algorithm) to identify general trends and best practices for training RL agents on semi-supervised offline datasets.

Generative models of biological sequences are a powerful tool for learning from complex sequence data, predicting the effects of mutations, and designing novel biomolecules with desired properties. To evaluate generative models it is important to accurately measure differences between high-dimensional distributions. In this paper we propose the ``KSD-B'', a novel divergence measure for distributions over biological sequences that is based on the kernelized Stein discrepancy (KSD). The KSD-B can be evaluated even when the normalizing constant of the model is unknown; it allows for variable length sequences and can take into account biological notions of sequence distance. Unlike previous KSDs over discrete spaces the KSD-B (a) is theoretically guaranteed to detect convergence and non-convergence of distributions over sequence space and (b) can be efficiently estimated in practice. We demonstrate the advantages of the KSD-B on problems with synthetic and real data, and apply it to measure the fit of state-of-the-art machine learning models. Overall, the KSD-B enables rigorous evaluation of generative biological sequence models, allowing the accuracy of models, sampling procedures, and library designs to be checked reliably.

In recent years, reinforcement learning (RL) has been applied to real-world problems with increasing success. Such applications often require to put constraints on the agent's behavior. Existing algorithms for constrained RL (CRL) rely on gradient descent-ascent, but this approach comes with a caveat. While these algorithms are guaranteed to converge on average, they do not guarantee last-iterate convergence, i.e., the current policy of the agent may never converge to the optimal solution. In practice, it is often observed that the policy alternates between satisfying the constraints and maximizing the reward, rarely accomplishing both objectives simultaneously. Here, we address this problem by introducing Reinforcement Learning with Optimistic Ascent-Descent (ReLOAD), a principled CRL method with guaranteed last-iterate convergence. We demonstrate its empirical effectiveness on a wide variety of CRL problems including discrete MDPs and continuous control. In the process we establish a benchmark of challenging CRL problems.

Generalization error always improves with more in-distribution data. However, it is an open question what happens as we add out-of-distribution (OOD) data. Intuitively, if the OOD data is quite different, it seems more data would harm generalization error, though if the OOD data are sufficiently similar, much empirical evidence suggests that OOD data can actually improve generalization error. We show a counter-intuitive phenomenon: the generalization error of a task can be a non-monotonic function of the amount of OOD data. Specifically, we prove that generalization error can improve with small amounts of OOD data, and then get worse than no OOD data with larger amounts. In other words, there is value in training on small amounts of OOD data. We analytically demonstrate these results via Fisher's Linear Discriminant on synthetic datasets, and empirically demonstrate them via deep networks on computer vision benchmarks such as MNIST, CIFAR-10, CINIC-10, PACS and DomainNet. In the idealistic setting where we know which samples are OOD, we show that these non-monotonic trends can be exploited using an appropriately weighted objective of the target and OOD empirical risk. While its practical utility is limited, this does suggest that if we can detect OOD samples, then there may be ways to benefit from them. When we do not know which samples are OOD, we show how a number of go-to strategies such as data-augmentation, hyper-parameter optimization and pre-training are not enough to ensure that the target generalization error does not deteriorate with the number of OOD samples in the dataset.

Research in the field of hyperparameter optimization (HPO) has been greatly accelerated by existing HPO benchmarks. Nonetheless, existing efforts in benchmarking all focus on HPO for traditional learning paradigms while ignoring federated learning (FL), a promising paradigm for collaboratively learning models from dispersed data. In this paper, we first identify some uniqueness of federated hyperparameter optimization (FedHPO) from various aspects, showing that existing HPO benchmarks no longer satisfy the need to study FedHPO methods. To facilitate the research of FedHPO, we propose and implement a benchmark suite FedHPO-Bench that incorporates comprehensive FedHPO problems, enables flexible customization of the function evaluations, and eases continuing extensions. We conduct extensive experiments based on FedHPO-Bench to provide the community with more insights into FedHPO. We open-sourced FedHPO-Bench at https://github.com/alibaba/FederatedScope/tree/master/benchmark/FedHPOBench.

We propose to minimize a generic differentiable objective with $L_1$ constraint using a simple reparametrization and straightforward stochastic gradient descent. Our proposal is the direct generalization of previous ideas that the $L_1$ penalty may be equivalent to a differentiable reparametrization with weight decay. We prove that the proposed method, spred, is an exact differentiable solver of $L_1$ and that the reparametrization trick is completely ``benign" for a generic nonconvex function. Practically, we demonstrate the usefulness of the method in (1) training sparse neural networks to perform gene selection tasks, which involves finding relevant features in a very high dimensional space, and (2) neural network compression task, to which previous attempts at applying the $L_1$-penalty have been unsuccessful. Conceptually, our result bridges the gap between the sparsity in deep learning and conventional statistical learning.