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In this paper, we study stochastic constrained minimax optimization problems with nonconvex-nonconcave structure, a central problem in modern machine learning, for which reliable and efficient algorithms remain largely unexplored due to its…

Optimization and Control · Mathematics 2026-02-25 Muhammad Khan , Yangyang Xu

Smooth minimax optimization problems play a central role in a wide range of applications, including machine learning, game theory, and operations research. However, existing algorithmic frameworks vary significantly depending on the problem…

Optimization and Control · Mathematics 2025-06-10 Taoli Zheng , Anthony Man-Cho So , Jiajin Li

We study (constrained) nonconvex (composite) optimization problems where the decision variables vector can be split into blocks of variables. Random block projection is a popular technique to handle this kind of problem for its remarkable…

Optimization and Control · Mathematics 2019-06-17 Zhan Yu , Daniel W. C. Ho

In this paper, we propose and analyze zeroth-order stochastic approximation algorithms for nonconvex and convex optimization, with a focus on addressing constrained optimization, high-dimensional setting and saddle-point avoiding. To handle…

Optimization and Control · Mathematics 2019-01-16 Krishnakumar Balasubramanian , Saeed Ghadimi

Alternating gradient-descent-ascent (AltGDA) is an optimization algorithm that has been widely used for model training in various machine learning applications, which aims to solve a nonconvex minimax optimization problem. However, the…

Machine Learning · Computer Science 2022-05-23 Ziyi Chen , Shaocong Ma , Yi Zhou

Optimizing large-scale nonconvex problems, common in deep learning, demands balancing rapid convergence with computational efficiency. First-order (FO) optimizers, which serve as today's baselines, provide fast convergence and good…

Machine Learning · Computer Science 2025-09-30 Jiahe Chen , Ziye Ma

This paper investigates the stochastic distributed nonconvex optimization problem of minimizing a global cost function formed by the summation of $n$ local cost functions. We solve such a problem by involving zeroth-order (ZO) information…

Optimization and Control · Mathematics 2021-10-15 Shengjun Zhang , Yunlong Dong , Dong Xie , Lisha Yao , Colleen P. Bailey , Shengli Fu

Recently, zeroth-order (ZO) optimization plays an essential role in scenarios where gradient information is inaccessible or unaffordable, such as black-box systems and resource-constrained environments. While existing adaptive methods such…

Machine Learning · Computer Science 2025-06-10 Yao Shu , Qixin Zhang , Kun He , Zhongxiang Dai

The conditional gradient idea proposed by Marguerite Frank and Philip Wolfe in 1956 was so well received by the community that new algorithms (also called Frank--Wolfe type algorithms) are still being actively created. In this paper, we…

Optimization and Control · Mathematics 2023-05-26 Aleksandr Lobanov , Anton Anikin , Alexander Gasnikov , Alexander Gornov , Sergey Chukanov

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

The adaptive momentum method (AdaMM), which uses past gradients to update descent directions and learning rates simultaneously, has become one of the most popular first-order optimization methods for solving machine learning problems.…

Machine Learning · Computer Science 2019-10-17 Xiangyi Chen , Sijia Liu , Kaidi Xu , Xingguo Li , Xue Lin , Mingyi Hong , David Cox

Zeroth-order optimization is the process of minimizing an objective $f(x)$, given oracle access to evaluations at adaptively chosen inputs $x$. In this paper, we present two simple yet powerful GradientLess Descent (GLD) algorithms that do…

Machine Learning · Computer Science 2020-05-20 Daniel Golovin , John Karro , Greg Kochanski , Chansoo Lee , Xingyou Song , Qiuyi Zhang

Stochastic optimization lies at the heart of machine learning, and its cornerstone is stochastic gradient descent (SGD), a method introduced over 60 years ago. The last 8 years have seen an exciting new development: variance reduction (VR)…

Machine Learning · Computer Science 2020-10-05 Robert M. Gower , Mark Schmidt , Francis Bach , Peter Richtarik

In this paper, we design and analyze a new family of adaptive subgradient methods for solving an important class of weakly convex (possibly nonsmooth) stochastic optimization problems. Adaptive methods that use exponential moving averages…

Optimization and Control · Mathematics 2020-05-26 Parvin Nazari , Davoud Ataee Tarzanagh , George Michailidis

We consider derivative-free algorithms for stochastic and non-stochastic convex optimization problems that use only function values rather than gradients. Focusing on non-asymptotic bounds on convergence rates, we show that if pairs of…

Optimization and Control · Mathematics 2014-08-21 John C. Duchi , Michael I. Jordan , Martin J. Wainwright , Andre Wibisono

Non-analytical objectives and constraints often arise in control systems, particularly in problems with complex dynamics, which are challenging yet lack efficient solution methods. In this work, we consider general constrained optimization…

Optimization and Control · Mathematics 2025-07-16 Yuke Zhou , Ruiyang Jin , Siyang Gao , Jianxiao Wang , Jie Song

Stochastic compositional minimax problems are prevalent in machine learning, yet there are only limited established on the convergence of this class of problems. In this paper, we propose a formal definition of the stochastic compositional…

Optimization and Control · Mathematics 2024-08-23 Yuyang Deng , Fuli Qiao , Mehrdad Mahdavi

We consider nonconvex-concave minimax optimization problems of the form $\min_{\bf x}\max_{\bf y\in{\mathcal Y}} f({\bf x},{\bf y})$, where $f$ is strongly-concave in $\bf y$ but possibly nonconvex in $\bf x$ and ${\mathcal Y}$ is a convex…

Machine Learning · Computer Science 2020-10-26 Luo Luo , Haishan Ye , Zhichao Huang , Tong Zhang

Nonconvex-concave min-max problem arises in many machine learning applications including minimizing a pointwise maximum of a set of nonconvex functions and robust adversarial training of neural networks. A popular approach to solve this…

Optimization and Control · Mathematics 2025-03-21 Jiawei Zhang , Peijun Xiao , Ruoyu Sun , Zhi-Quan Luo

In this work we address the problem of convex optimization in a multi-agent setting where the objective is to minimize the mean of local cost functions whose derivatives are not available (e.g. black-box models). Moreover agents can only…

Optimization and Control · Mathematics 2023-06-14 Alessio Maritan , Luca Schenato