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Related papers: Zeroth-Order Algorithms for Nonconvex Minimax Prob…

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We propose stochastic optimization algorithms that can find local minima faster than existing algorithms for nonconvex optimization problems, by exploiting the third-order smoothness to escape non-degenerate saddle points more efficiently.…

Optimization and Control · Mathematics 2017-12-19 Yaodong Yu , Pan Xu , Quanquan Gu

This paper considers the nonconvex nonsmooth problem in which the objective function is Lipschitz continuous. We focus on the stochastic setting where the algorithm can access stochastic function value evaluations with heavy-tailed noise,…

Machine Learning · Computer Science 2026-05-26 Zhuanghua Liu , Luo Luo

In this paper, we consider a stochastic distributed nonconvex optimization problem with the cost function being distributed over $n$ agents having access only to zeroth-order (ZO) information of the cost. This problem has various machine…

Optimization and Control · Mathematics 2022-01-11 Xinlei Yi , Shengjun Zhang , Tao Yang , Karl H. Johansson

This paper investigates how to accelerate the convergence of distributed optimization algorithms on nonconvex problems with zeroth-order information available only. We propose a zeroth-order (ZO) distributed primal-dual stochastic…

Optimization and Control · Mathematics 2021-10-15 Shengjun Zhang , Colleen P. Bailey

We consider non-smooth saddle point optimization problems. To solve these problems, we propose a zeroth-order method under bounded or Lipschitz continuous noise, possible adversarial. In contrast to the state-of-the-art algorithms, our…

Optimization and Control · Mathematics 2023-03-28 Darina Dvinskikh , Vladislav Tominin , Yaroslav Tominin , Alexander Gasnikov

This paper addresses stochastic optimization of Lipschitz-continuous, nonsmooth and nonconvex objectives over compact convex sets, where only noisy function evaluations are available. While gradient-free methods have been developed for…

Optimization and Control · Mathematics 2025-08-26 Anik Kumar Paul , Shalabh Bhatnagar

Stochastic optimization problems with unknown decision-dependent distributions have attracted increasing attention in recent years due to its importance in applications. Since the gradient of the objective function is inaccessible as a…

Optimization and Control · Mathematics 2025-10-30 Yuya Hikima , Akiko Takeda

In this thesis, I study the minimax oracle complexity of distributed stochastic optimization. First, I present the "graph oracle model", an extension of the classic oracle complexity framework that can be applied to study distributed…

Optimization and Control · Mathematics 2021-09-03 Blake Woodworth

Analysis of Stochastic Gradient Descent (SGD) and its variants typically relies on the assumption of uniformly bounded variance, a condition that frequently fails in practical non-convex settings, such as neural network training, as well as…

Machine Learning · Computer Science 2026-04-21 Arda Fazla , Ege C. Kaya , Antesh Upadhyay , Abolfazl Hashemi

This paper introduces a novel Homogeneous Second-order Descent Ascent (HSDA) algorithm for nonconvex-strongly concave minimax optimization problems. At each iteration, HSDA uniquely computes a search direction by solving a homogenized…

Optimization and Control · Mathematics 2026-02-17 Jia-Hao Chen , Zi Xu , Hui-Ling Zhang

In the paper, we propose a class of accelerated zeroth-order and first-order momentum methods for both nonconvex mini-optimization and minimax-optimization. Specifically, we propose a new accelerated zeroth-order momentum (Acc-ZOM) method…

Optimization and Control · Mathematics 2022-01-19 Feihu Huang , Shangqian Gao , Jian Pei , Heng Huang

This paper is devoted to solving a convex stochastic optimization problem in a overparameterization setup for the case where the original gradient computation is not available, but an objective function value can be computed. For this class…

Optimization and Control · Mathematics 2024-02-14 Aleksandr Lobanov , Alexander Gasnikov

Gradient descent and its variants are widely used in machine learning. However, oracle access of gradient may not be available in many applications, limiting the direct use of gradient descent. This paper proposes a method of estimating…

Optimization and Control · Mathematics 2019-10-07 Qinbo Bai , Mridul Agarwal , Vaneet Aggarwal

This paper considers zeroth-order optimization for stochastic convex minimization problem. We propose a parameter-free stochastic zeroth-order method (POEM) by introducing a step-size scheme based on the distance over finite difference and…

Optimization and Control · Mathematics 2025-05-06 Kunjie Ren , Luo Luo

Rapid advances in data collection and processing capabilities have allowed for the use of increasingly complex models that give rise to nonconvex optimization problems. These formulations, however, can be arbitrarily difficult to solve in…

Multiagent Systems · Computer Science 2020-04-01 Stefan Vlaski , Ali H. Sayed

Constrained non-convex optimization is fundamentally challenging, as global solutions are generally intractable and constraint qualifications may not hold. However, in many applications, including safe policy optimization in control and…

Optimization and Control · Mathematics 2025-11-14 Ilyas Fatkhullin , Niao He , Guanghui Lan , Florian Wolf

We study the complexity of producing $(\delta,\epsilon)$-stationary points of Lipschitz objectives which are possibly neither smooth nor convex, using only noisy function evaluations. Recent works proposed several stochastic zero-order…

Optimization and Control · Mathematics 2024-04-16 Guy Kornowski , Ohad Shamir

We provide a unified analysis of two-timescale gradient descent ascent (TTGDA) for solving structured nonconvex minimax optimization problems in the form of $\min_\textbf{x} \max_{\textbf{y} \in Y} f(\textbf{x}, \textbf{y})$, where the…

Machine Learning · Computer Science 2025-01-28 Tianyi Lin , Chi Jin , Michael. I. Jordan

Nonsmooth nonconvex-concave minimax problems have attracted significant attention due to their wide applications in many fields. In this paper, we consider a class of nonsmooth nonconvex-concave minimax problems on Riemannian manifolds.…

Optimization and Control · Mathematics 2026-03-24 Xiyuan Xie , Qia Li

Derivative-free optimization has become an important technique used in machine learning for optimizing black-box models. To conduct updates without explicitly computing gradient, most current approaches iteratively sample a random search…

Machine Learning · Statistics 2018-08-03 Liu Liu , Minhao Cheng , Cho-Jui Hsieh , Dacheng Tao