ICML 2023 Papers

Coordinate denoising is a promising 3D molecular pre-training method, which has achieved remarkable performance in various downstream drug discovery tasks. Theoretically, the objective is equivalent to learning the force field, which is revealed helpful for downstream tasks. Nevertheless, there are two challenges for coordinate denoising to learn an effective force field, i.e. low coverage samples and isotropic force field. The underlying reason is that molecular distributions assumed by existing denoising methods fail to capture the anisotropic characteristic of molecules. To tackle these challenges, we propose a novel hybrid noise strategy, including noises on both dihedral angel and coordinate. However, denoising such hybrid noise in a traditional way is no more equivalent to learning the force field. Through theoretical deductions, we find that the problem is caused by the dependency of the input conformation for covariance. To this end, we propose to decouple the two types of noise and design a novel fractional denoising method (Frad), which only denoises the latter coordinate part. In this way, Frad enjoys both the merits of sampling more low-energy structures and the force field equivalence. Extensive experiments show the effectiveness of Frad in molecule representation, with a new state-of-the-art on 9 out of 12 tasks of QM9 and on 7 out of 8 targets of MD17.

We consider a contextual combinatorial bandit problem where in each round a learning agent selects a subset of arms and receives feedback on the selected arms according to their scores. The score of an arm is an unknown function of the arm's feature. Approximating this unknown score function with deep neural networks, we propose algorithms: Combinatorial Neural UCB ($\texttt{CN-UCB}$) and Combinatorial Neural Thompson Sampling ($\texttt{CN-TS}$). We prove that $\texttt{CN-UCB}$ achieves $\tilde{\mathcal{O}}(\tilde{d} \sqrt{T})$ or $\tilde{\mathcal{O}}(\sqrt{\tilde{d} T K})$ regret, where $\tilde{d}$ is the effective dimension of a neural tangent kernel matrix, $K$ is the size of a subset of arms, and $T$ is the time horizon. For $\texttt{CN-TS}$, we adapt an optimistic sampling technique to ensure the optimism of the sampled combinatorial action, achieving a worst-case (frequentist) regret of $\tilde{\mathcal{O}}(\tilde{d} \sqrt{TK})$. To the best of our knowledge, these are the first combinatorial neural bandit algorithms with regret performance guarantees. In particular, $\texttt{CN-TS}$ is the first Thompson sampling algorithm with the worst-case regret guarantees for the general contextual combinatorial bandit problem. The numerical experiments demonstrate the superior performances of our proposed algorithms.

Symbolic regression (SR) is the problem of learning a symbolic expression from numerical data. Recently, deep neural models trained on procedurally-generated synthetic datasets showed competitive performance compared to more classical Genetic Programming (GP) ones. Unlike their GP counterparts, these neural approaches are trained to generate expressions from datasets given as context. This allows them to produce accurate expressions in a single forward pass at test time. However, they usually do not benefit from search abilities, which result in low performance compared to GP on out-of-distribution datasets. In this paper, we propose a novel method which provides the best of both worlds, based on a Monte-Carlo Tree Search procedure using a context-aware neural mutation model, which is initially pre-trained to learn promising mutations, and further refined from successful experiences in an online fashion. The approach demonstrates state-of-the-art performance on the well-known SRBench benchmark.

Multi-player online games depict the interaction of multiple players with each other over time. Strongly monotone games are of particular interest since they have benign properties and also relate to many classic games that have applications in real life. Existing works mainly focus on the time-invariant case with provable guarantees established. However, the research of the more general *time-varying* games in changing environments is underexplored and the best-known result cannot match the guarantees in the time-invariant case. In this work, we present a new decentralized online algorithm for time-varying strongly monotone games, which greatly improves existing results and obtains fast rates, matching the best time-invariant guarantee without knowing the environmental non-stationarity. Furthermore, to achieve faster rates, we generalize the RVU property with smoothness and establish a series of problem-dependent bounds that also match the best time-invariant one. To realize all those results, we make a comprehensive use of the techniques in non-stationary and universal online learning.

Parameter inference, i.e. inferring the posterior distribution of the parameters of a statistical model given some data, is a central problem to many scientific disciplines. Posterior inference with generative models is an alternative to methods such as Markov Chain Monte Carlo, both for likelihood-based and simulation-based inference. However, assessing the accuracy of posteriors encoded in generative models is not straightforward. In this paper, we introduce "Tests of Accuracy with Random Points" (TARP) coverage testing as a method to estimate coverage probabilities of generative posterior estimators. Our method differs from previously-existing coverage-based methods, which require posterior evaluations. We prove that our approach is necessary and sufficient to show that a posterior estimator is accurate. We demonstrate the method on a variety of synthetic examples, and show that TARP can be used to test the results of posterior inference analyses in high-dimensional spaces. We also show that our method can detect inaccurate inferences in cases where existing methods fail.

Various optimal gradient-based algorithms have been developed for smooth nonconvex optimization. However, many nonconvex machine learning problems do not belong to the class of smooth functions and therefore the existing algorithms are sub-optimal. Instead, these problems have been shown to satisfy certain generalized-smooth conditions, which have not been well understood in the existing literature. In this paper, we propose a notion of $\alpha$-symmetric generalized-smoothness that substantially extends the existing notions and covers many important functions such as high-order polynomials and exponential functions. We study the fundamental properties and establish descent lemmas for the functions in this class. Then, to solve such a large class of nonconvex problems, we design a special deterministic normalized gradient descent algorithm that achieves the optimal iteration complexity $\mathcal{O}(\epsilon^{-2})$, and also prove that the popular SPIDER variance reduction algorithm achieves the optimal sample complexity $\mathcal{O}(\epsilon^{-3})$. Our results show that solving generalized-smooth nonconvex problems is as efficient as solving smooth nonconvex problems.

This paper studies the challenging continual learning (CL) setting of Class Incremental Learning (CIL). CIL learns a sequence of tasks consisting of disjoint sets of concepts or classes. At any time, a single model is built that can be applied to predict/classify test instances of any classes learned thus far without providing any task related information for each test instance. Although many techniques have been proposed for CIL, they are mostly empirical. It has been shown recently that a strong CIL system needs a strong within-task prediction (WP) and a strong out-of-distribution (OOD) detection for each task. However, it is still not known whether CIL is actually learnable. This paper shows that CIL is learnable. Based on the theory, a new CIL algorithm is also proposed. Experimental results demonstrate its effectiveness.

Horizon dependence is an important difference between reinforcement learning and other machine learning paradigms. Yet, existing results tackling the (exact) horizon dependence either assume that the reward is bounded per step, introducing unfair comparison, or assume strict total boundedness that requires the sum of rewards to be bounded *almost surely* -- allowing only restricted noise on the reward observation. This paper addresses these limitations by introducing a new relaxation -- *expected boundedness* on rewards, where we allow the reward to be stochastic with only boundedness on the *expected* sum -- opening the door to study horizon-dependence with a much broader set of reward functions with noises. We establish a novel generic algorithm that achieves *no-horizon dependence* in terms of sample complexity for both Markov Decision Processes (MDP) and Games, via reduction to a good-conditioned *auxiliary Markovian environment*, in which only ``important'' state-action pairs are preserved. The algorithm takes only $\tilde{O}(\frac{S^2A}{\epsilon^2})$ episodes interacting with such an environment to achieve an $\epsilon$-optimal policy/strategy (with high probability), improving (zhang, 2022) (which only applies to MDPs with deterministic rewards). Here $S$ is the number of states and $A$ is the number of actions, and the bound is independent of the horizon $H$.

Model-based reinforcement learning (RL) often achieves higher sample efficiency in practice than model-free RL by learning a dynamics model to generate samples for policy learning. Previous works learn a dynamics model that fits under the empirical state-action visitation distribution for all historical policies, i.e., the sample replay buffer. However, in this paper, we observe that fitting the dynamics model under the distribution for *all historical policies* does not necessarily benefit model prediction for the *current policy* since the policy in use is constantly evolving over time. The evolving policy during training will cause state-action visitation distribution shifts. We theoretically analyze how this distribution shift over historical policies affects the model learning and model rollouts. We then propose a novel dynamics model learning method, named *Policy-adapted Dynamics Model Learning (PDML)*. PDML dynamically adjusts the historical policy mixture distribution to ensure the learned model can continually adapt to the state-action visitation distribution of the evolving policy. Experiments on a range of continuous control environments in MuJoCo show that PDML achieves significant improvement in sample efficiency and higher asymptotic performance combined with the state-of-the-art model-based RL methods.

We investigate the extent to which offline demonstration data can improve online learning. It is natural to expect some improvement, but *the question is how, and by how much?* We show that the degree of improvement must depend on the *quality* of the demonstration data. To generate portable insights, we focus on Thompson sampling (TS) applied to a multi-armed bandit as a prototypical online learning algorithm and model. The demonstration data is generated by an expert with a given *competence* level, a notion we introduce. We propose an informed TS algorithm that utilizes the demonstration data in a coherent way through Bayes' rule and derive a prior-dependent Bayesian regret bound. This offers insight into how pretraining can greatly improve online performance and how the degree of improvement increases with the expert's competence level. We also develop a practical, approximate informed TS algorithm through Bayesian bootstrapping and show substantial empirical regret reduction through experiments.

Recently, the contrastive language-image pre-training, e.g., CLIP, has demonstrated promising results on various downstream tasks. The pre-trained model can capture enriched visual concepts for images by learning from a large scale of text-image data. However, transferring the learned visual knowledge to open-vocabulary semantic segmentation is still under-explored. In this paper, we propose a CLIP-based model named SegCLIP for the topic of open-vocabulary segmentation in an annotation-free manner. The SegCLIP achieves segmentation based on ViT and the main idea is to gather patches with learnable centers to semantic regions through training on text-image pairs. The gathering operation can dynamically capture the semantic groups, which can be used to generate the final segmentation results. We further propose a reconstruction loss on masked patches and a superpixel-based KL loss with pseudo-labels to enhance the visual representation. Experimental results show that our model achieves comparable or superior segmentation accuracy on the PASCAL VOC 2012 (+0.3% mIoU), PASCAL Context (+2.3% mIoU), and COCO (+2.2% mIoU) compared with baselines. We release the code at https://github.com/ArrowLuo/SegCLIP.

We study preferential Bayesian optimization (BO) where reliable feedback is limited to pairwise comparison called duels. An important challenge in preferential BO, which uses the preferential Gaussian process (GP) model to represent flexible preference structure, is that the posterior distribution is a computationally intractable skew GP. The most widely used approach for preferential BO is Gaussian approximation, which ignores the skewness of the true posterior. Alternatively, Markov chain Monte Carlo (MCMC) based preferential BO is also proposed. In this work, we first verify the accuracy of Gaussian approximation, from which we reveal the critical problem that the predictive probability of duels can be inaccurate. This observation motivates us to improve the MCMC-based estimation for skew GP, for which we show the practical efficiency of Gibbs sampling and derive the low variance MC estimator. However, the computational time of MCMC can still be a bottleneck in practice. Towards building a more practical preferential BO, we develop a new method that achieves both high computational efficiency and low sample complexity, and then demonstrate its effectiveness through extensive numerical experiments.

Deep reinforcement learning (RL) is a powerful approach for solving optimal control problems. However, RL-trained policies often suffer from the action fluctuation problem, where the consecutive actions significantly differ despite only slight state variations. This problem results in mechanical components' wear and tear and poses safety hazards. The action fluctuation is caused by the high Lipschitz constant of actor networks. To address this problem, we propose a neural network named LipsNet. We propose the Multi-dimensional Gradient Normalization (MGN) method, to constrain the Lipschitz constant of networks with multi-dimensional input and output. Benefiting from MGN, LipsNet achieves Lipschitz continuity, allowing smooth actions while preserving control performance by adjusting Lipschitz constant. LipsNet addresses the action fluctuation problem at network level rather than algorithm level, which can serve as actor networks in most RL algorithms, making it more flexible and user-friendly than previous works. Experiments demonstrate that LipsNet has good landscape smoothness and noise robustness, resulting in significantly smoother action compared to the Multilayer Perceptron.

Training classifiers is difficult with severe class imbalance, but many rare events are the culmination of a sequence with much more common intermediate outcomes. For example, in online marketing a user first sees an ad, then may click on it, and finally may make a purchase; estimating the probability of purchases is difficult because of their rarity. We show both theoretically and through data experiments that the more abundant data in earlier steps may be leveraged to improve estimation of probabilities of rare events. We present PRESTO, a relaxation of the proportional odds model for ordinal regression. Instead of estimating weights for one separating hyperplane that is shifted by separate intercepts for each of the estimated Bayes decision boundaries between adjacent pairs of categorical responses, we estimate separate weights for each of these transitions. We impose an L1 penalty on the differences between weights for the same feature in adjacent weight vectors in order to shrink towards the proportional odds model. We prove that PRESTO consistently estimates the decision boundary weights under a sparsity assumption. Synthetic and real data experiments show that our method can estimate rare probabilities in this setting better than both logistic regression on the rare category, which fails to borrow strength from more abundant categories, and the proportional odds model, which is too inflexible.

Loss functions serve as the foundation of supervised learning and are often chosen prior to model development. To avoid potentially ad hoc choices of losses, statistical decision theory describes a desirable property for losses known as *properness*, which asserts that Bayes' rule is optimal. Recent works have sought to *learn losses* and models jointly. Existing methods do this by fitting an inverse canonical link function which monotonically maps $\mathbb{R}$ to $[0,1]$ to estimate probabilities for binary problems. In this paper, we extend monotonicity to maps between $\mathbb{R}^{C-1}$ and the projected probability simplex $\tilde{\Delta}^{C-1}$ by using monotonicity of gradients of convex functions. We present LegendreTron as a novel and practical method that jointly learns *proper canonical losses* and probabilities for multiclass problems. Tested on a benchmark of domains with up to 1,000 classes, our experimental results show that our method consistently outperforms the natural multiclass baseline under a $t$-test at 99% significance on all datasets with greater than $10$ classes.

Adversarial training, which is to enhance robustness against adversarial attacks, has received much attention because it is easy to generate human-imperceptible perturbations of data to deceive a given deep neural network. In this paper, we propose a new adversarial training algorithm that is theoretically well motivated and empirically superior to other existing algorithms. A novel feature of the proposed algorithm is to apply more regularization to data vulnerable to adversarial attacks than other existing regularization algorithms do. Theoretically, we show that our algorithm can be understood as an algorithm of minimizing a newly derived upper bound of the robust risk. Numerical experiments illustrate that our proposed algorithm improves the generalization (accuracy on examples) and robustness (accuracy on adversarial attacks) simultaneously to achieve the state-of-the-art performance.

Providing generalization guarantees for modern neural networks has been a crucial task in statistical learning. Recently, several studies have attempted to analyze the generalization error in such settings by using tools from fractal geometry. While these works have successfully introduced new mathematical tools to apprehend generalization, they heavily rely on a Lipschitz continuity assumption, which in general does not hold for neural networks and might make the bounds vacuous. In this work, we address this issue and prove fractal geometry-based generalization bounds without requiring any Lipschitz assumption. To achieve this goal, we build up on a classical covering argument in learning theory and introduce a data-dependent fractal dimension. Despite introducing a significant amount of technical complications, this new notion lets us control the generalization error (over either fixed or random hypothesis spaces) along with certain mutual information (MI) terms. To provide a clearer interpretation to the newly introduced MI terms, as a next step, we introduce a notion of `geometric stability' and link our bounds to the prior art. Finally, we make a rigorous connection between the proposed data-dependent dimension and topological data analysis tools, which then enables us to compute the dimension in a numerically efficient way. We support our theory with experiments conducted on various settings.

This paper revisits Gaussian Mixture Copula Model (GMCM), a more expressive alternative to the widely used Gaussian Mixture Model (GMM), with the goal to make its parameter estimation tractable. Both the Expectation Maximization and the direct Likelihood Maximization frameworks for GMCM have to grapple with a likelihood function that lacks a closed form. This has led to a few approximation schemes that alleviate the problem, nonetheless leaving the issue still unresolved. Additionally, past works have alluded to an additional challenge of parameter non-identifiability, but none has offered a rigorous treatment and a commensurate solution framework to overcome the same. This work offers solutions to each of these issues in an attempt to help GMCM realize its full potential. The source of non-identifiability is not only proven but also suitable priors are proposed that eliminate the problem. Additionally, an efficient numerical framework is proposed to evaluate the intractable likelihood function, while also providing its analytical derivatives. Finally, a view of GMCM as a series of bijective mappings from a base distribution is presented, which paves the way to synthesize GMCM using modern, probabilistic programming languages (PPLs). The main claims of this work are supported by empirical evidence gathered on synthetic and real-world datasets.

Sketching is one of the most fundamental tools in large-scale machine learning. It enables runtime and memory saving via randomly compressing the original large problem into lower dimensions. In this paper, we propose a novel sketching scheme for the first order method in large-scale distributed learning setting, such that the communication costs between distributed agents are saved while the convergence of the algorithms is still guaranteed. Given gradient information in a high dimension $d$, the agent passes the compressed information processed by a sketching matrix $R\in \mathbb{R}^{s\times d}$ with $s\ll d$, and the receiver de-compressed via the de-sketching matrix $R^\top$ to ``recover'' the information in original dimension. Using such a framework, we develop algorithms for federated learning with lower communication costs. However, such random sketching does not protect the privacy of local data directly. We show that the gradient leakage problem still exists after applying the sketching technique by presenting a specific gradient attack method. As a remedy, we prove rigorously that the algorithm will be differentially private by adding additional random noises in gradient information, which results in a both communication-efficient and differentially private first order approach for federated learning tasks. Our sketching scheme can be further generalized to other learning settings and might be of independent interest itself.