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We consider the case of derivative-free algorithms for non-convex optimization, also known as zero order algorithms, that use only function evaluations rather than gradients. For a wide variety of gradient approximators based on finite…

Optimization and Control · Mathematics 2019-10-30 Lampros Flokas , Emmanouil-Vasileios Vlatakis-Gkaragkounis , Georgios Piliouras

We provide a framework for computing the exact worst-case performance of any algorithm belonging to a broad class of oracle-based first-order methods for composite convex optimization, including those performing explicit, projected,…

Optimization and Control · Mathematics 2019-11-22 Adrien B. Taylor , Julien M. Hendrickx , François Glineur

In this paper, we study oracle-efficient algorithms for beyond worst-case analysis of online learning. We focus on two settings. First, the smoothed analysis setting of [RST11,HRS22] where an adversary is constrained to generating samples…

Machine Learning · Computer Science 2022-11-23 Nika Haghtalab , Yanjun Han , Abhishek Shetty , Kunhe Yang

We develop stochastic first-order primal-dual algorithms to solve a class of convex-concave saddle-point problems. When the saddle function is strongly convex in the primal variable, we develop the first stochastic restart scheme for this…

Optimization and Control · Mathematics 2021-04-13 Renbo Zhao

The article is devoted to the development of algorithmic methods ensuring efficient complexity bounds for strongly convex-concave saddle point problems in the case when one of the groups of variables is high-dimensional, and the other is…

Optimization and Control · Mathematics 2022-10-26 Egor Gladin , Ilya Kuruzov , Fedor Stonyakin , Dmitry Pasechnyuk , Mohammad Alkousa , Alexander Gasnikov

We consider stochastic optimization problems in multi-agent settings, where a network of agents aims to learn parameters which are optimal in terms of a global objective, while giving preference to locally observed streaming information. To…

Multiagent Systems · Computer Science 2017-05-24 Alec Koppel , Brian M. Sadler , Alejandro Ribeiro

We study the SAM (Sharpness-Aware Minimization) optimizer which has recently attracted a lot of interest due to its increased performance over more classical variants of stochastic gradient descent. Our main contribution is the derivation…

Machine Learning · Computer Science 2023-06-06 Enea Monzio Compagnoni , Luca Biggio , Antonio Orvieto , Frank Norbert Proske , Hans Kersting , Aurelien Lucchi

This paper resolves a longstanding open question pertaining to the design of near-optimal first-order algorithms for smooth and strongly-convex-strongly-concave minimax problems. Current state-of-the-art first-order algorithms find an…

Optimization and Control · Mathematics 2021-07-27 Tianyi Lin , Chi Jin , Michael. I. Jordan

In this work, we focuses on the following saddle point problem $\min_x \max_y p(x) + R(x,y) - q(y)$ where $R(x,y)$ is $L_R$-smooth, $\mu_x$-strongly convex, $\mu_y$-strongly concave and $p(x), q(y)$ are convex and $L_p, L_q$-smooth…

Optimization and Control · Mathematics 2023-07-25 Ekaterina Borodich , Georgiy Kormakov , Dmitry Kovalev , Aleksandr Beznosikov , Alexander Gasnikov

Stochastic saddle point (SSP) problems are, in general, less studied compared to stochastic minimization problems. However, SSP problems emerge from machine learning (adversarial training, e.g., GAN, AUC maximization), statistics (robust…

Optimization and Control · Mathematics 2023-12-14 Vitali Pirau

Recent years have witnessed a growing interest in the topic of min-max optimization, owing to its relevance in the context of generative adversarial networks (GANs), robust control and optimization, and reinforcement learning. Motivated by…

Machine Learning · Computer Science 2022-04-08 Arman Adibi , Aritra Mitra , George J. Pappas , Hamed Hassani

Learning to optimize - the idea that we can learn from data algorithms that optimize a numerical criterion - has recently been at the heart of a growing number of research efforts. One of the most challenging issues within this approach is…

Machine Learning · Computer Science 2018-02-21 Louis Faury , Flavian Vasile

Optimal Transport (OT) naturally arises in many machine learning applications, yet the heavy computational burden limits its wide-spread uses. To address the scalability issue, we propose an implicit generative learning-based framework…

Machine Learning · Computer Science 2019-06-26 Yujia Xie , Minshuo Chen , Haoming Jiang , Tuo Zhao , Hongyuan Zha

Stochastic nonconvex-concave min-max saddle point problems appear in many machine learning and control problems including distributionally robust optimization, generative adversarial networks, and adversarial learning. In this paper, we…

Optimization and Control · Mathematics 2023-09-12 Morteza Boroun , Zeinab Alizadeh , Afrooz Jalilzadeh

We consider strongly convex-concave minimax problems in the federated setting, where the communication constraint is the main bottleneck. When clients are arbitrarily heterogeneous, a simple Minibatch Mirror-prox achieves the best…

Machine Learning · Computer Science 2021-02-15 Charlie Hou , Kiran K. Thekumparampil , Giulia Fanti , Sewoong Oh

This work is devoted to solving the composite optimization problem with the mixture oracle: for the smooth part of the problem, we have access to the gradient, and for the non-smooth part, only the one-point zero-order oracle is available.…

Optimization and Control · Mathematics 2025-07-23 Aleksandr Beznosikov , Ivan Stepanov , Artyom Voronov , Alexander Gasnikov

We study a class of convex-concave saddle-point problems of the form $\min_x\max_y \langle Kx,y\rangle+f_{\cal{P}}(x)-h^\ast(y)$ where $K$ is a linear operator, $f_{\cal{P}}$ is the sum of a convex function $f$ with a Lipschitz-continuous…

Optimization and Control · Mathematics 2021-06-07 Vladimir Kolmogorov , Thomas Pock

Despite its important applications in Machine Learning, min-max optimization of nonconvex-nonconcave objectives remains elusive. Not only are there no known first-order methods converging even to approximate local min-max points, but the…

Computational Complexity · Computer Science 2020-09-22 Constantinos Daskalakis , Stratis Skoulakis , Manolis Zampetakis

A method for locating first order saddle points on the energy surface of a magnetic system is described and several applications presented where the mechanism of various magnetic transitions is identified. The starting point for the…

Computational Physics · Physics 2025-01-17 Hendrik Schrautzer , Moritz Sallermann , Pavel F. Bessarab , Hannes Jónsson

We extend the Frank-Wolfe (FW) optimization algorithm to solve constrained smooth convex-concave saddle point (SP) problems. Remarkably, the method only requires access to linear minimization oracles. Leveraging recent advances in FW…

Optimization and Control · Mathematics 2017-03-07 Gauthier Gidel , Tony Jebara , Simon Lacoste-Julien