NeurIPS 2023 论文列表

In this paper, we revisit the bilevel optimization problem, in which the upper-level objective function is generally nonconvex and the lower-level objective function is strongly convex. Although this type of problem has been studied extensively, it still remains an open question how to achieve an $\mathcal{O}(\epsilon^{-1.5})$ sample complexity in Hessian/Jacobian-free stochastic bilevel optimization without any second-order derivative computation. To fill this gap, we propose a novel Hessian/Jacobian-free bilevel optimizer named FdeHBO, which features a simple fully single-loop structure, a projection-aided finite-difference Hessian/Jacobian-vector approximation, and momentum-based updates. Theoretically, we show that FdeHBO requires $\mathcal{O}(\epsilon^{-1.5})$ iterations (each using $\mathcal{O}(1)$ samples and only first-order gradient information) to find an $\epsilon$-accurate stationary point. As far as we know, this is the first Hessian/Jacobian-free method with an $\mathcal{O}(\epsilon^{-1.5})$ sample complexity for nonconvex-strongly-convex stochastic bilevel optimization.

Offline model-based optimization aims to find a design that maximizes a property of interest using only an offline dataset, with applications in robot, protein, and molecule design, among others. A prevalent approach is gradient ascent, where a proxy model is trained on the offline dataset and then used to optimize the design. This method suffers from an out-of-distribution issue, where the proxy is not accurate for unseen designs. To mitigate this issue, we explore using a pseudo-labeler to generate valuable data for fine-tuning the proxy. Specifically, we propose $\textit{\textbf{I}mportance-aware \textbf{C}o-\textbf{T}eaching for Offline Model-based Optimization}~(\textbf{ICT})$. This method maintains three symmetric proxies with their mean ensemble as the final proxy, and comprises two steps. The first step is $\textit{pseudo-label-driven co-teaching}$. In this step, one proxy is iteratively selected as the pseudo-labeler for designs near the current optimization point, generating pseudo-labeled data. Subsequently, a co-teaching process identifies small-loss samples as valuable data and exchanges them between the other two proxies for fine-tuning, promoting knowledge transfer. This procedure is repeated three times, with a different proxy chosen as the pseudo-labeler each time, ultimately enhancing the ensemble performance. To further improve accuracy of pseudo-labels, we perform a secondary step of $\textit{meta-learning-based sample reweighting}$, which assigns importance weights to samples in the pseudo-labeled dataset and updates them via meta-learning. ICT achieves state-of-the-art results across multiple design-bench tasks, achieving the best mean rank $3.1$ and median rank $2$ among $15$ methods. Our source code can be accessed here.

In reinforcement learning, robust policies for high-stakes decision-making problems with limited data are usually computed by optimizing the percentile criterion. The percentile criterion is optimized by constructing an uncertainty set that contains the true model with high probability and optimizing the policy for the worst model in the set. Since the percentile criterion is non-convex, constructing these sets itself is challenging. Existing works use Bayesian credible regions as uncertainty sets, but they are often unnecessarily large and result in learning overly conservative policies. To overcome these shortcomings, we propose a novel Value-at-Risk based dynamic programming algorithm to optimize the percentile criterion without explicitly constructing any uncertainty sets. Our theoretical and empirical results show that our algorithm implicitly constructs much smaller uncertainty sets and learns less-conservative robust policies.

We consider the problem of minimizing a continuous function given given access to a natural quantum generalization of a stochastic gradient oracle. We provide two new methods for the special case of minimizing a Lipschitz convex function. Each method obtains a dimension versus accuracy trade-off which is provably unachievable classically and we prove that one method is asymptotically optimal in low-dimensional settings. Additionally, we provide quantum algorithms for computing a critical point of a smooth non-convex function at rates not known to be achievable classically. To obtain these results we build upon the quantum multivariate mean estimation result of Cornelissen et al. and provide a general quantum variance reduction technique of independent interest.

Stochastic Gradient Descent (SGD) is arguably the most important single algorithm in modern machine learning. Although SGD with unbiased gradient estimators has been studied extensively over at least half a century, SGD variants relying on biased estimators are rare. Nevertheless, there has been an increased interest in this topic in recent years. However, existing literature on SGD with biased estimators lacks coherence since each new paper relies on a different set of assumptions, without any clear understanding of how they are connected, which may lead to confusion. We address this gap by establishing connections among the existing assumptions, and presenting a comprehensive map of the underlying relationships. Additionally, we introduce a new set of assumptions that is provably weaker than all previous assumptions, and use it to present a thorough analysis of BiasedSGD in both convex and non-convex settings, offering advantages over previous results. We also provide examples where biased estimators outperform their unbiased counterparts or where unbiased versions are simply not available. Finally, we demonstrate the effectiveness of our framework through experimental results that validate our theoretical findings.

Deep reinforcement learning agents for continuous control are known to exhibit significant instability in their performance over time. In this work, we provide a fresh perspective on these behaviors by studying the return landscape: the mapping between a policy and a return. We find that popular algorithms traverse noisy neighborhoods of this landscape, in which a single update to the policy parameters leads to a wide range of returns. By taking a distributional view of these returns, we map the landscape, characterizing failure-prone regions of policy space and revealing a hidden dimension of policy quality. We show that the landscape exhibits surprising structure by finding simple paths in parameter space which improve the stability of a policy. To conclude, we develop a distribution-aware procedure which finds such paths, navigating away from noisy neighborhoods in order to improve the robustness of a policy. Taken together, our results provide new insight into the optimization, evaluation, and design of agents.

In many applications, learning systems are required to process continuous non-stationary data streams. We study this problem in an online learning framework and propose an algorithm that can deal with adversarial time-varying and nonlinear constraints. As we show in our work, the algorithm called Constraint Violation Velocity Projection (CVV-Pro) achieves $\sqrt{T}$ regret and converges to the feasible set at a rate of $1/\sqrt{T}$, despite the fact that the feasible set is slowly time-varying and a priori unknown to the learner. CVV-Pro only relies on local sparse linear approximations of the feasible set and therefore avoids optimizing over the entire set at each iteration, which is in sharp contrast to projected gradients or Frank-Wolfe methods. We also empirically evaluate our algorithm on two-player games, where the players are subjected to a shared constraint.

Most of existing neural methods for multi-objective combinatorial optimization (MOCO) problems solely rely on decomposition, which often leads to repetitive solutions for the respective subproblems, thus a limited Pareto set. Beyond decomposition, we propose a novel neural heuristic with diversity enhancement (NHDE) to produce more Pareto solutions from two perspectives. On the one hand, to hinder duplicated solutions for different subproblems, we propose an indicator-enhanced deep reinforcement learning method to guide the model, and design a heterogeneous graph attention mechanism to capture the relations between the instance graph and the Pareto front graph. On the other hand, to excavate more solutions in the neighborhood of each subproblem, we present a multiple Pareto optima strategy to sample and preserve desirable solutions. Experimental results on classic MOCO problems show that our NHDE is able to generate a Pareto front with higher diversity, thereby achieving superior overall performance. Moreover, our NHDE is generic and can be applied to different neural methods for MOCO.

Various gradient compression algorithms have been proposed to alleviate the communication bottleneck in distributed learning, and they have demonstrated effectiveness in terms of high compression ratios and theoretical low communication complexity. However, when it comes to practically training modern deep neural networks (DNNs), these algorithms have yet to match the inference performance of uncompressed SGD-momentum (SGDM) and adaptive optimizers (e.g.,Adam). More importantly, recent studies suggest that these algorithms actually offer no speed advantages over SGDM/Adam when used with common distributed DNN training frameworks ( e.g., DistributedDataParallel (DDP)) in the typical settings, due to heavy compression/decompression computation or incompatibility with the efficient All-Reduce or the requirement of uncompressed warmup at the early stage. For these reasons, we propose a novel 1-bit adaptive optimizer, dubbed *Bi*nary *r*andomization a*d*aptive optimiz*er* (**Birder**). The quantization of Birder can be easily and lightly computed, and it does not require warmup with its uncompressed version in the beginning. Also, we devise Hierarchical-1-bit-All-Reduce to further lower the communication volume. We theoretically prove that it promises the same convergence rate as the Adam. Extensive experiments, conducted on 8 to 64 GPUs (1 to 8 nodes) using DDP, demonstrate that Birder achieves comparable inference performance to uncompressed SGDM/Adam, with up to ${2.5 \times}$ speedup for training ResNet-50 and ${6.3\times}$ speedup for training BERT-Base. Code is publicly available at https://openi.pcl.ac.cn/c2net_optim/Birder.

This paper studies delayed stochastic algorithms for weakly convex optimization in a distributed network with workers connected to a master node. Recently, Xu~et~al.~2022 showed that an inertial stochastic subgradient method converges at a rate of $\mathcal{O}(\tau_{\text{max}}/\sqrt{K})$ which depends on the maximum information delay $\tau_{\text{max}}$. In this work, we show that the delayed stochastic subgradient method ($\texttt{DSGD}$) obtains a tighter convergence rate which depends on the expected delay $\bar{\tau}$. Furthermore, for an important class of composition weakly convex problems, we develop a new delayed stochastic prox-linear ($\texttt{DSPL}$) method in which the delays only affect the high-order term in the rate and hence, are negligible after a certain number of $\texttt{DSPL}$ iterations. In addition, we demonstrate the robustness of our proposed algorithms against arbitrary delays. By incorporating a simple safeguarding step in both methods, we achieve convergence rates that depend solely on the number of workers, eliminating the effect of delays. Our numerical experiments further confirm the empirical superiority of our proposed methods.

Internal measures that are used to assess the quality of a clustering usually take into account intra-group and/or inter-group criteria. There are many papers in the literature that propose algorithms with provable approximation guarantees for optimizing the former. However, the optimization of inter-group criteria is much less understood. Here, we contribute to the state-of-the-art of this literature by devising algorithms with provable guarantees for the maximization of two natural inter-group criteria, namely the minimum spacing and the minimum spanning tree spacing. The former is the minimum distance between points in different groups while the latter captures separability through the cost of the minimum spanning tree that connects all groups. We obtain results for both the unrestricted case, in which no constraint on the clusters is imposed, and for the constrained case where each group is required to have a minimum number of points. Our constraint is motivated by the fact that the popular Single-Linkage, which optimizes both criteria in the unrestricted case, produces clustering with many tiny groups. To complement our work, we present an empirical study with 10 real datasets that provides evidence that our methods work very well in practical settings.

In this paper, we study the conditional stochastic optimization (CSO) problem which covers a variety of applications including portfolio selection, reinforcement learning, robust learning, causal inference, etc. The sample-averaged gradient of the CSO objective is biased due to its nested structure, and therefore requires a high sample complexity for convergence. We introduce a general stochastic extrapolation technique that effectively reduces the bias. We show that for nonconvex smooth objectives, combining this extrapolation with variance reduction techniques can achieve a significantly better sample complexity than the existing bounds. Additionally, we develop new algorithms for the finite-sum variant of the CSO problem that also significantly improve upon existing results. Finally, we believe that our debiasing technique has the potential to be a useful tool for addressing similar challenges in other stochastic optimization problems.

Exploration is one of the main challenges in Reinforcement Learning (RL), especially in environments with sparse rewards. Learning from Demonstrations (LfD) is a promising approach to solving this problem by leveraging expert demonstrations. However, expert demonstrations of high quality are usually costly or even impossible to collect in real-world applications. In this work, we propose a novel RL algorithm called HYbrid Policy Optimization (HYPO), which uses a small number of imperfect demonstrations to accelerate an agent's online learning process. The key idea is to train an offline guider policy using imitation learning in order to instruct an online agent policy to explore efficiently. Through mutual update of the guider policy and the agent policy, the agent can leverage suboptimal demonstrations for efficient exploration while avoiding the conservative policy caused by imperfect demonstrations. Empirical results show that HYPO significantly outperforms several baselines in various challenging tasks, such as MuJoCo with sparse rewards, Google Research Football, and the AirSim drone simulation.

Adaptive methods with non-diagonal preconditioning have shown state-of-the-art results on various tasks. However, their computational complexity and memory requirement makes it challenging to scale these methods to modern neural network architectures. To address this challenge, some previous works have adopted block-diagonal preconditioners. However, the memory cost of storing the block-diagonal matrix remains substantial, leading to the use of smaller block sizes and ultimately resulting in suboptimal performance. To reduce the time and memory complexity without sacrificing performance, we propose approximating each diagonal block of the second moment matrix by low-rank matrices and enforcing the same basis for the blocks within each layer. We provide theoretical justification for such sharing and design an algorithm to efficiently maintain this shared-basis block low-rank approximation during training. Our results on a deep autoencoder and a transformer benchmark demonstrate that the proposed method outperforms first-order methods with slightly more time and memory usage, while also achieving competitive or superior performance compared to other second-order methods with less time and memory usage.

We propose a novel formulation for dictionary learning that minimizes the determinant of the dictionary matrix, also known as its volume, subject to the constraint that each row of the sparse coefficient matrix has unit $\ell_1$ norm. The main motivation for the proposed formulation is that it provides global identifiability guarantee of the groundtruth dictionary and sparse coefficient matrices, up to the inherent and inconsequential permutation and scaling ambiguity, if a set of vectors obtained from the coefficient matrix lies inside the $\ell_\infty$ norm ball but contains the $\ell_2$ norm ball in their convex hull. Unlike existing work on identifiability of dictionary learning, our result is global, meaning that a globally optimal solution to our proposed formulation has to be a permuted and rescaled version of the groundtruth factors. Another major improvement in our result is that there is no additional assumption on the dictionary matrix other than it is nonsingular, unlike most other work that require the atoms of the dictionary to be mutually incoherent. We also provide a probabilistic analysis and show that if the sparse coefficient matrix is generated from the widely adopted Bernoulli-Gaussian model, then it is globally identifiable if the sample size is bigger than a constant times $k\log k$, where $k$ is the number atoms in the dictionary, with overwhelming probability. The bound is essentially the same as those local identifiability results, but we show that it is also global. Finally, we propose algorithms to solve the new proposed formulation, specifically one based on the linearized-ADMM with efficient per-iteration updates. The proposed algorithms exhibit surprisingly effective performance in correctly and efficiently recovering the dictionary, as demonstrated in the numerical experiments.

Feature visualization has gained significant popularity as an explainability method, particularly after the influential work by Olah et al. in 2017. Despite its success, its widespread adoption has been limited due to issues in scaling to deeper neural networks and the reliance on tricks to generate interpretable images. Here, we describe MACO, a simple approach to address these shortcomings. It consists in optimizing solely an image's phase spectrum while keeping its magnitude constant to ensure that the generated explanations lie in the space of natural images. Our approach yields significantly better results -- both qualitatively and quantitatively -- unlocking efficient and interpretable feature visualizations for state-of-the-art neural networks. We also show that our approach exhibits an attribution mechanism allowing to augment feature visualizations with spatial importance. Furthermore, we enable quantitative evaluation of feature visualizations by introducing 3 metrics: transferability, plausibility, and alignment with natural images. We validate our method on various applications and we introduce a website featuring MACO visualizations for all classes of the ImageNet dataset, which will be made available upon acceptance. Overall, our study unlocks feature visualizations for the largest, state-of-the-art classification networks without resorting to any parametric prior image model, effectively advancing a field that has been stagnating since 2017 (Olah et al, 2017).

Functional constrained optimization (FCO) has emerged as a powerful tool for solving various machine learning problems. However, with the rapid increase in applications of neural networks in recent years, it has become apparent that both the objective and constraints often involve nonconvex functions, which poses significant challenges in obtaining high-quality solutions. In this work, we focus on a class of nonconvex FCO problems with nonconvex constraints, where the two optimization variables are nonlinearly coupled in the inequality constraint. Leveraging the primal-dual optimization framework, we propose a smoothed first-order Lagrangian method (SLM) for solving this class of problems. We establish the theoretical convergence guarantees of SLM to the Karush-Kuhn-Tucker (KKT) solutions through quantifying dual error bounds. By establishing connections between this structured FCO and equilibrium-constrained nonconvex problems (also known as bilevel optimization), we apply the proposed SLM to tackle bilevel optimization oriented problems where the lower-level problem is nonconvex. Numerical results obtained from both toy examples and hyper-data cleaning problems demonstrate the superiority of SLM compared to benchmark methods.

This paper investigates group distributionally robust optimization (GDRO), with the purpose to learn a model that performs well over $m$ different distributions. First, we formulate GDRO as a stochastic convex-concave saddle-point problem, and demonstrate that stochastic mirror descent (SMD), using $m$ samples in each iteration, achieves an $O(m (\log m)/\epsilon^2)$ sample complexity for finding an $\epsilon$-optimal solution, which matches the $\Omega(m/\epsilon^2)$ lower bound up to a logarithmic factor. Then, we make use of techniques from online learning to reduce the number of samples required in each round from $m$ to $1$, keeping the same sample complexity. Specifically, we cast GDRO as a two-players game where one player simply performs SMD and the other executes an online algorithm for non-oblivious multi-armed bandits. Next, we consider a more practical scenario where the number of samples that can be drawn from each distribution is different, and propose a novel formulation of weighted GDRO, which allows us to derive distribution-dependent convergence rates. Denote by $n_i$ the sample budget for the $i$-th distribution, and assume $n_1 \geq n_2 \geq \cdots \geq n_m$. In the first approach, we incorporate non-uniform sampling into SMD such that the sample budget is satisfied in expectation, and prove that the excess risk of the $i$-th distribution decreases at an $O(\sqrt{n_1 \log m}/n_i)$ rate. In the second approach, we use mini-batches to meet the budget exactly and also reduce the variance in stochastic gradients, and then leverage stochastic mirror-prox algorithm, which can exploit small variances, to optimize a carefully designed weighted GDRO problem. Under appropriate conditions, it attains an $O((\log m)/\sqrt{n_i})$ convergence rate, which almost matches the optimal $O(\sqrt{1/n_i})$ rate of only learning from the $i$-th distribution with $n_i$ samples.

In the first-order query model for zero-sum $K\times K$ matrix games, players observe the expected pay-offs for all their possible actions under the randomized action played by their opponent. This classical model has received renewed interest after the discovery by Rakhlin and Sridharan that $\epsilon$-approximate Nash equilibria can be computed efficiently from $O(\frac{\ln K}{\epsilon})$ instead of $O(\frac{\ln K}{\epsilon^2})$ queries. Surprisingly, the optimal number of such queries, as a function of both $\epsilon$ and $K$, is not known. We make progress on this question on two fronts. First, we fully characterise the query complexity of learning exact equilibria ($\epsilon=0$), by showing that they require a number of queries that is linear in $K$, which means that it is essentially as hard as querying the whole matrix, which can also be done with $K$ queries. Second, for $\epsilon > 0$, the current query complexity upper bound stands at $O(\min(\frac{\ln(K)}{\epsilon} , K))$. We argue that, unfortunately, obtaining a matching lower bound is not possible with existing techniques: we prove that no lower bound can be derived by constructing hard matrices whose entries take values in a known countable set, because such matrices can be fully identified by a single query. This rules out, for instance, reducing to an optimization problem over the hypercube by encoding it as a binary payoff matrix. We then introduce a new technique for lower bounds, which allows us to obtain lower bounds of order $\tilde\Omega(\log(\frac{1}{K\epsilon})$ for any $\epsilon \leq 1 / (cK^4)$, where $c$ is a constant independent of $K$. We further discuss possible future directions to improve on our techniques in order to close the gap with the upper bounds.