ICML 2023 论文列表

Quantum computing is an emerging technology that has been rapidly advancing in the past decades. In this paper, we conduct a systematic study of quantum lower bounds on finding $\epsilon$-approximate stationary points of nonconvex functions, and we consider the following two important settings: 1) having access to $p$-th order derivatives; or 2) having access to stochastic gradients. The classical query lower bounds are $\Omega\big(\epsilon^{-\frac{1+p}{p}}\big)$ regarding the first setting and $\Omega(\epsilon^{-4})$ regarding the second setting (or $\Omega(\epsilon^{-3})$ if the stochastic gradient function is mean-squared smooth). In this paper, we extend all these classical lower bounds to the quantum setting. They match the classical algorithmic results respectively, demonstrating that there is no quantum speedup for finding $\epsilon$-stationary points of nonconvex functions with $p$-th order derivative inputs or stochastic gradient inputs, whether with or without the mean-squared smoothness assumption. Technically, we prove our quantum lower bounds by showing that the sequential nature of classical hard instances in all these settings also applies to quantum queries, preventing any quantum speedup other than revealing information of the stationary points sequentially.

Solving large-scale multistage stochastic programming (MSP) problems poses a significant challenge as commonly used stagewise decomposition algorithms, including stochastic dual dynamic programming (SDDP), face growing time complexity as the subproblem size and problem count increase. Traditional approaches approximate the value functions as piecewise linear convex functions by incrementally accumulating subgradient cutting planes from the primal and dual solutions of stagewise subproblems. Recognizing these limitations, we introduce TranSDDP, a novel Transformer-based stagewise decomposition algorithm. This innovative approach leverages the structural advantages of the Transformer model, implementing a sequential method for integrating subgradient cutting planes to approximate the value function. Through our numerical experiments, we affirm TranSDDP's effectiveness in addressing MSP problems. It efficiently generates a piecewise linear approximation for the value function, significantly reducing computation time while preserving solution quality, thus marking a promising progression in the treatment of large-scale multistage stochastic programming problems.

We study the problem of constrained efficient global optimization, where both the objective and constraints are expensive black-box functions that can be learned with Gaussian processes. We propose CONFIG (CONstrained efFIcient Global Optimization), a simple and effective algorithm to solve it. Under certain regularity assumptions, we show that our algorithm enjoys the same cumulative regret bound as that in the unconstrained case and similar cumulative constraint violation upper bounds. For commonly used Matern and Squared Exponential kernels, our bounds are sublinear and allow us to derive a convergence rate to the optimal solution of the original constrained problem. In addition, our method naturally provides a scheme to declare infeasibility when the original black-box optimization problem is infeasible. Numerical experiments on sampled instances from the Gaussian process, artificial numerical problems, and a black-box building controller tuning problem all demonstrate the competitive performance of our algorithm. Compared to the other state-of-the-art methods, our algorithm significantly improves the theoretical guarantees while achieving competitive empirical performance.

Bilevel optimization recently has received tremendous attention due to its great success in solving important machine learning problems like meta learning, reinforcement learning, and hyperparameter optimization. Extending single-agent training on bilevel problems to the decentralized setting is a natural generalization, and there has been a flurry of work studying decentralized bilevel optimization algorithms. However, it remains unknown how to design the distributed algorithm with sample complexity and convergence rate comparable to SGD for stochastic optimization, and at the same time without directly computing the exact Hessian or Jacobian matrices. In this paper we propose such an algorithm. More specifically, we propose a novel decentralized stochastic bilevel optimization (DSBO) algorithm that only requires first order stochastic oracle, Hessian-vector product and Jacobian-vector product oracle. The sample complexity of our algorithm matches the currently best known results for DSBO, while our algorithm does not require estimating the full Hessian and Jacobian matrices, thereby possessing to improved per-iteration complexity.

In this work we focus our attention on distributed optimization problems in the context where the communication time between the server and the workers is non-negligible. We obtain novel methods supporting bidirectional compression (both from the server to the workers and vice versa) that enjoy new state-of-the-art theoretical communication complexity for convex and nonconvex problems. Our bounds are the first that manage to decouple the variance/error coming from the workers-to-server and server-to-workers compression, transforming a multiplicative dependence to an additive one. Moreover, in the convex regime, we obtain the first bounds that match the theoretical communication complexity of gradient descent. Even in this convex regime, our algorithms work with biased gradient estimators, which is non-standard and requires new proof techniques that may be of independent interest. Finally, our theoretical results are corroborated through suitable experiments.

We study the problem of approximating stationary points of Lipschitz and smooth functions under $(\varepsilon,\delta)$-differential privacy (DP) in both the finite-sum and stochastic settings. A point $\widehat{w}$ is called an $\alpha$-stationary point of a function $F:\mathbb{R}^d\rightarrow\mathbb{R}$ if $\|\nabla F(\widehat{w})\|\leq \alpha$. We give a new construction that improves over the existing rates in the stochastic optimization setting, where the goal is to find approximate stationary points of the population risk given $n$ samples. Our construction finds a $\tilde{O}\big(\frac{1}{n^{1/3}} + \big[\frac{\sqrt{d}}{n\varepsilon}\big]^{1/2}\big)$-stationary point of the population risk in time linear in $n$. We also provide an efficient algorithm that finds an $\tilde{O}\big(\big[\frac{\sqrt{d}}{n\varepsilon}\big]^{2/3}\big)$-stationary point in the finite-sum setting. This improves on the previous best rate of $\tilde{O}\big(\big[\frac{\sqrt{d}}{n\varepsilon}\big]^{1/2}\big)$. Furthermore, under the additional assumption of convexity, we completely characterize the sample complexity of finding stationary points of the population risk (up to polylog factors) and show that the optimal rate on population stationarity is $\tilde \Theta\big(\frac{1}{\sqrt{n}}+\frac{\sqrt{d}}{n\varepsilon}\big)$. Finally, we show that our methods can be used to provide dimension-independent rates of $O\big(\frac{1}{\sqrt{n}}+\min\big(\big[\frac{\sqrt{rank}}{n\varepsilon}\big]^{2/3},\frac{1}{(n\varepsilon)^{2/5}}\big)\big)$ on population stationarity for Generalized Linear Models (GLM), where $rank$ is the rank of the design matrix, which improves upon the previous best known rate.

Zero-order (ZO) optimization is a powerful tool for dealing with realistic constraints. On the other hand, the gradient-tracking (GT) technique proved to be an efficient method for distributed optimization aiming to achieve consensus. However, it is a first-order (FO) method that requires knowledge of the gradient, which is not always possible in practice. In this work, we introduce a zero-order distributed optimization method based on a one-point estimate of the gradient tracking technique. We prove that this new technique converges with a single noisy function query at a time in the non-convex setting. We then establish a convergence rate of $O(\frac{1}{\sqrt[3]{K}})$ after a number of iterations K, which competes with that of $O(\frac{1}{\sqrt[4]{K}})$ of its centralized counterparts. Finally, a numerical example validates our theoretical results.

Policy Optimization (PO) is one of the most popular methods in Reinforcement Learning (RL). Thus, theoretical guarantees for PO algorithms have become especially important to the RL community. In this paper, we study PO in adversarial MDPs with a challenge that arises in almost every real-world application -- *delayed bandit feedback*. We give the first near-optimal regret bounds for PO in tabular MDPs, and may even surpass state-of-the-art (which uses less efficient methods). Our novel Delay-Adapted PO (DAPO) is easy to implement and to generalize, allowing us to extend our algorithm to: (i) infinite state space under the assumption of linear $Q$-function, proving the first regret bounds for delayed feedback with function approximation. (ii) deep RL, demonstrating its effectiveness in experiments on MuJoCo domains.

Data imbalance is a common problem in machine learning that can have a critical effect on the performance of a model. Various solutions exist but their impact on the convergence of the learning dynamics is not understood. Here, we elucidate the significant negative impact of data imbalance on learning, showing that the learning curves for minority and majority classes follow sub-optimal trajectories when training with a gradient-based optimizer. This slowdown is related to the imbalance ratio and can be traced back to a competition between the optimization of different classes. Our main contribution is the analysis of the convergence of full-batch (GD) and stochastic gradient descent (SGD), and of variants that renormalize the contribution of each per-class gradient. We find that GD is not guaranteed to decrease the loss for each class but that this problem can be addressed by performing a per-class normalization of the gradient. With SGD, class imbalance has an additional effect on the direction of the gradients: the minority class suffers from a higher directional noise, which reduces the effectiveness of the per-class gradient normalization. Our findings not only allow us to understand the potential and limitations of strategies involving the per-class gradients, but also the reason for the effectiveness of previously used solutions for class imbalancesuch as oversampling.

Despite the effectiveness of ELECTRA-style pre-training, their performance is dependent on the careful selection of the model size for the auxiliary generator, leading to high trial-and-error costs. In this paper, we present the first systematic study of this problem. Our theoretical investigation highlights the importance of controlling the generator capacity in ELECTRA-style training. Meanwhile, we found it is *not* handled properly in the original ELECTRA design, leading to the sensitivity issue. Specifically, since adaptive optimizers like Adam will cripple the weighing of individual losses in the joint optimization, the original design fails to control the generator training effectively. To regain control over the generator, we modularize the generator optimization by decoupling the generator optimizer and discriminator optimizer completely, instead of simply relying on the weighted objective combination. Our simple technique reduced the sensitivity of ELECTRA training significantly and obtains considerable performance gain compared to the original design.

The goal of offline black-box optimization (BBO) is to optimize an expensive black-box function using a fixed dataset of function evaluations. Prior works consider forward approaches that learn surrogates to the black-box function and inverse approaches that directly map function values to corresponding points in the input domain of the black-box function. These approaches are limited by the quality of the offline dataset and the difficulty in learning one-to-many mappings in high dimensions, respectively. We propose Denoising Diffusion Optimization Models (DDOM), a new inverse approach for offline black-box optimization based on diffusion models. Given an offline dataset, DDOM learns a conditional generative model over the domain of the black-box function conditioned on the function values. We investigate several design choices in DDOM, such as reweighting the dataset to focus on high function values and the use of classifier-free guidance at test-time to enable generalization to function values that can even exceed the dataset maxima. Empirically, we conduct experiments on the Design-Bench benchmark (Trabucco et al., 2022) and show that DDOM achieves results competitive with state-of-the-art baselines.

We consider the problem of global optimization with noisy zeroth order oracles — a well-motivated problem useful for various applications ranging from hyper-parameter tuning for deep learning to new material design. Existing work relies on Gaussian processes or other non-parametric family, which suffers from the curse of dimensionality. In this paper, we propose a new algorithm GO-UCB that leverages a parametric family of functions (e.g., neural networks) instead. Under a realizable assumption and a few other mild geometric conditions, we show that GO-UCB achieves a cumulative regret of $\tilde{O}(\sqrt{T})$ where $T$ is the time horizon. At the core of GO-UCB is a carefully designed uncertainty set over parameters based on gradients that allows optimistic exploration. Synthetic and real-world experiments illustrate GO-UCB works better than popular Bayesian optimization approaches, even if the model is misspecified.

We define a new class of set functions that in addition to being monotone and subadditive, also admit a very limited form of submodularity defined over a permutation of the ground set. We refer to this permutation as a submodular order. We give fast algorithms with strong approximation guarantees for maximizing submodular order functions under a variety of constraints. Applying this new notion to the problem of constrained assortment optimization in fundamental choice models, we obtain new algorithms that are both faster and have stronger approximation guarantees (in some cases, first algorithm with constant factor guarantee). We also show an intriguing connection to the maximization of monotone submodular functions in the streaming model, where we recover best known approximation guarantees as a corollary of our results.

Negative and positive curvatures affect optimization in different ways. However, a lot of existing optimization theories are based on the Lipschitz smoothness assumption, which cannot differentiate between the two. In this paper, we propose to use two separate assumptions for positive and negative curvatures, so that we can study the different implications of the two. We analyze the Lookahead and Local SGD methods as concrete examples. Both of them require multiple copies of model parameters and communication among them for every certain period of time in order to prevent divergence. We show that the minimum communication frequency is inversely proportional to the negative curvature, and when the negative curvature becomes zero, we recover the existing theory results for convex optimization. Finally, both experimentally and theoretically, we demonstrate that modern neural networks have highly unbalanced positive/negative curvatures. Thus, an analysis based on separate positive and negative curvatures is more pertinent.

In humans' classroom learning, many effective study techniques (e.g., the Feynman technique, peer questioning, etc.) have been developed to improve learning outcomes. We are interested in investigating whether these techniques can inspire the development of ML training strategies to improve bi-level optimization (BLO) based methods. Towards this goal, we develop a general framework, Skillearn, which consists of basic elements such as learners, interaction functions, learning stages, etc. These elements can be flexibly configured to create various training strategies, each emulating a study technique of humans. In case studies, we apply Skillearn to create new training strategies, by emulating the Feynman technique and peer questioning, which are two broadly adopted techniques in humans' classroom learning. These training strategies are used for improving two BLO based applications including neural architecture search and data weighting. Experiments on various datasets demonstrate the effectiveness of our methods.

The notion of omnipredictors (Gopalan, Kalai, Reingold, Sharan and Wieder ITCS 2022), suggested a new paradigm for loss minimization. Rather than learning a predictor based on a known loss function, omnipredictors can easily be post-processed to minimize any one of a rich family of loss functions compared with the loss of hypotheses in a class $\mathcal C$. It has been shown that such omnipredictors exist and are implied (for all convex and Lipschitz loss functions) by the notion of multicalibration from the algorithmic fairness literature. In this paper, we introduce omnipredictors for constrained optimization and study their complexity and implications. The notion that we introduce allows the learner to be unaware of the loss function that will be later assigned *as well as the constraints that will be later imposed*, as long as the subpopulations that are used to define these constraints are known. We show how to obtain omnipredictors for constrained optimization problems, relying on appropriate variants of multicalibration. We also investigate the implications of this notion when the constraints used are so-called group fairness notions.

Optimizing user engagement is a key goal for modern recommendation systems, but blindly pushing users towards increased consumption risks burn-out, churn, or even addictive habits. To promote digital well-being, most platforms now offer a service that periodically prompts users to take breaks. These, however, must be set up manually, and so may be suboptimal for both users and the system. In this paper, we study the role of breaks in recommendation, and propose a framework for learning optimal breaking policies that promote and sustain long-term engagement. Based on the notion that recommendation dynamics are susceptible to both positive and negative feedback, we cast recommendation as a Lotka-Volterra dynamical system, where breaking reduces to a problem of optimal control. We then give an efficient learning algorithm, provide theoretical guarantees, and empirically demonstrate the utility of our approach on semi-synthetic data.

Federated Averaging (FedAvg) and its variants are the most popular optimization algorithms in federated learning (FL). Previous convergence analyses of FedAvg either assume full client participation or partial client participation where the clients can be uniformly sampled. However, in practical cross-device FL systems, only a subset of clients that satisfy local criteria such as battery status, network connectivity, and maximum participation frequency requirements (to ensure privacy) are available for training at a given time. As a result, client availability follows a *natural cyclic pattern*. We provide (to our knowledge) the first theoretical framework to analyze the convergence of FedAvg with cyclic client participation with several different client optimizers such as GD, SGD, and shuffled SGD. Our analysis discovers that cyclic client participation can achieve a faster asymptotic convergence rate than vanilla FedAvg with uniform client participation under suitable conditions, providing valuable insights into the design of client sampling protocols.

Distributed training of large deep neural networks requires frequent exchange of massive data between machines, thus communication efficiency is a major concern. Existing compressed communication methods are either not compatible with large batch optimization algorithms, or do not provide sufficient speedup in large scale. In this paper, we combine sparsification-based gradient compression with the layer-wise adaptive moments optimizer for large batch training (LAMB). We propose SLAMB, a novel communication-efficient optimizer that supports large batch sizes and scales to thousands of GPUs. SLAMB employs momentum masking, local error compensation, and element-wise adaptive rescaling to achieve accurate layer-wise weight updates, which translates to fast convergence for very large batches. Our empirical results show that, compared to the state-of-the-art, SLAMB transmits half the amount of data in large-batch BERT pre-training, without sacrificing accuracy. Moreover, SLAMB achieves excellent scalability in large computing infrastructures. For instance, SLAMB with 128 GPUs reduces the training time of Swin Transformer pre-training on ImageNet to 5.35 hours, which is 2 hours faster than the state-of-the-art. At the extreme, we trained BERT-XL (2.8B parameters) on 1,024 NVIDIA A100 GPUs, where SLAMB achieved 90% scaling efficiency.