Related papers: Statistical Mechanics of Min-Max Problems

The min-max optimization problem, also known as the saddle point problem, is a classical optimization problem which is also studied in the context of zero-sum games. Given a class of objective functions, the goal is to find a value for the…

Many applications in machine learning can be framed as minimization problems and solved efficiently using gradient-based techniques. However, recent applications of generative models, particularly GANs, have triggered interest in solving…

Distributed optimization is an important direction of research in modern optimization theory. Its applications include large scale machine learning, distributed signal processing and many others. The paper studies decentralized min-max…

Min-max saddle point games have recently been intensely studied, due to their wide range of applications, including training Generative Adversarial Networks (GANs). However, most of the recent efforts for solving them are limited to special…

The rise of computer vision applications in the real world puts the security of the deep neural networks at risk. Recent works demonstrate that convolutional neural networks are susceptible to adversarial examples - where the input images…

Recent focus on robustness to adversarial attacks for deep neural networks produced a large variety of algorithms for training robust models. Most of the effective algorithms involve solving the min-max optimization problem for training…

We study a variant of a recently introduced min-max optimization framework where the max-player is constrained to update its parameters in a greedy manner until it reaches a first-order stationary point. Our equilibrium definition for this…

Variational inequalities are a formalism that includes games, minimization, saddle point, and equilibrium problems as special cases. Methods for variational inequalities are therefore universal approaches for many applied tasks, including…

In this work we study a special minimax problem where there are linear constraints that couple both the minimization and maximization decision variables. The problem is a generalization of the traditional saddle point problem (which does…

This thesis investigates the design of algorithms for solving min-max optimization problems, which form the mathematical foundation of many modern applications in machine learning, game theory, and optimization. This work offers new…

Classically, a mainstream approach for solving a convex-concave min-max problem is to instead solve the variational inequality problem arising from its first-order optimality conditions. Is it possible to solve min-max problems faster by…

This paper proposes an asymmetric perturbation technique for solving bilinear saddle-point optimization problems, commonly arising in minimax problems, game theory, and constrained optimization. Perturbing payoffs or values is known to be…

The use of min-max optimization in adversarial training of deep neural network classifiers and training of generative adversarial networks has motivated the study of nonconvex-nonconcave optimization objectives, which frequently arise in…

We study MinMax solution methods for a general class of optimization problems related to (and including) optimal transport. Theoretically, the focus is on fitting a large class of problems into a single MinMax framework and generalizing…

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…

Adversarial formulations such as generative adversarial networks (GANs) have rekindled interest in two-player min-max games. A central obstacle in the optimization of such games is the rotational dynamics that hinder their convergence. In…

First-order methods for minimization and saddle point (min-max) problems are widely used for solving large-scale problems, in particular arising in machine learning. The majority of works obtain favorable complexity guarantees of such…

In this article, we dwell into the class of so-called ill-posed Linear Inverse Problems (LIP) which simply refers to the task of recovering the entire signal from its relatively few random linear measurements. Such problems arise in a…

Delays and asynchrony are inevitable in large-scale machine-learning problems where communication plays a key role. As such, several works have extensively analyzed stochastic optimization with delayed gradients. However, as far as we are…

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…