Related papers: Statistical Mechanics of Min-Max Problems

Despite the rich existing literature about minimax optimization in continuous settings, only very partial results of this kind have been obtained for combinatorial settings. In this paper, we fill this gap by providing a characterization of…

Adversarial optimal transport has been proven useful as a mathematical formulation to model resource allocation problems to maximize the efficiency of transportation with an adversary, who modifies the data. It is often the case, however,…

Majorization-minimization algorithms consist of iteratively minimizing a majorizing surrogate of an objective function. Because of its simplicity and its wide applicability, this principle has been very popular in statistics and in signal…

In this paper, we consider multi-objective reinforcement learning, which arises in many real-world problems with multiple optimization goals. We approach the problem with a max-min framework focusing on fairness among the multiple goals and…

In this paper, we present novel randomized algorithms for solving saddle point problems whose dual feasible region is given by the direct product of many convex sets. Our algorithms can achieve an ${\cal O}(1/N)$ and ${\cal O}(1/N^2)$ rate…

An universal primal-dual approach of description equilibriums in large class of hierarchical congestion population games is proposed. At the very core of the approach is hierarchy of enclosed to each other transport networks. In different…

In this tutorial, we provide an introduction to machine learning methods for finding Nash equilibria in games with large number of agents. These types of problems are important for the operations research community because of their…

Machine Learning algorithms are typically regarded as appropriate optimization schemes for minimizing risk functions that are constructed on the training set, which conveys statistical flavor to the corresponding learning problem. When the…

This paper studies the connections between mean-field games and the social welfare optimization problems. We consider a mean field game in functional spaces with a large population of agents, each of which seeks to minimize an individual…

A long line of works characterizes the sample complexity of regret minimization in sequential decision-making by min-max programs. In the corresponding saddle-point game, the min-player optimizes the sampling distribution against an…

Convergence to a saddle point for convex-concave functions has been studied for decades, while recent years has seen a surge of interest in non-convex (zero-sum) smooth games, motivated by their recent wide applications. It remains an…

We study a class of statistical inverse problems with non-linear pointwise operators motivated by concrete statistical applications. A two-step procedure is proposed, where the first step smoothes the data and inverts the non-linearity.…

We develop a general framework for estimating function-valued parameters under equality or inequality constraints in infinite-dimensional statistical models. Such constrained learning problems are common across many areas of statistics and…

We consider a statistical inverse learning problem, where we observe the image of a function $f$ through a linear operator $A$ at i.i.d. random design points $X_i$, superposed with an additive noise. The distribution of the design points is…

Min-max optimization problems involving nonconvex-nonconcave objectives have found important applications in adversarial training and other multi-agent learning settings. Yet, no known gradient descent-based method is guaranteed to converge…

This paper provides necessary and sufficient conditions for a pair of randomised stopping times to form a saddle point of a zero-sum Dynkin game with partial and/or asymmetric information across players. The framework is non-Markovian and…

Adversarial training, a special case of multi-objective optimization, is an increasingly prevalent machine learning technique: some of its most notable applications include GAN-based generative modeling and self-play techniques in…

This monograph presents a theoretical background and a broad introduction to the Min-Max Framework for Majorization-Minimization (MM4MM), an algorithmic methodology for solving minimization problems by formulating them as min-max problems…

In this paper we develop optimal algorithms in the binary-forking model for a variety of fundamental problems, including sorting, semisorting, list ranking, tree contraction, range minima, and ordered set union, intersection and difference.…

Some recent works in machine learning and computer vision involve the solution of a bi-level optimization problem. Here the solution of a parameterized lower-level problem binds variables that appear in the objective of an upper-level…