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Many efficient algorithms have been designed to recover Nash equilibria of various classes of finite games. Special classes of continuous games with infinite strategy spaces, such as polynomial games, can be solved by semidefinite…
Using convex combination and linesearch techniques, we introduce a novel primal-dual algorithm for solving structured convex-concave saddle point problems with a generic smooth nonbilinear coupling term. Our adaptive linesearch strategy…
We consider two classes of constrained finite state-action stochastic games. First, we consider a two player nonzero sum single controller constrained stochastic game with both average and discounted cost criterion. We consider the same…
In this paper, the generalized Nash equilibrium (GNE) seeking problem for continuous games with coupled affine inequality constraints is investigated in a partial-decision information scenario, where each player can only access its…
This paper introduces a novel payoff-based learning scheme for distributed optimization in repeatedly-played strategic-form games. Standard reinforcement-based learning exhibits several limitations with respect to their asymptotic…
This paper presents a new primal-dual method for computing an equilibrium of generalized (continuous) Nash game (referred to as generalized Nash equilibrium problem (GNEP)) where each player's feasible strategy set depends on the other…
This paper proposes a new differentially private distributed Nash equilibrium seeking algorithm for aggregative games under time-varying unbalanced directed communication graphs. Random independent Laplace noises are injected into the…
In this paper, we aim to develop distributed continuous-time algorithms over directed graphs to seek the Nash equilibrium in a noncooperative game. Motivated by the recent consensus-based designs, we present a distributed algorithm with a…
In this paper, we study zeroth-order algorithms for nonconvex minimax problems with coupled linear constraints under the deterministic and stochastic settings, which have attracted wide attention in machine learning, signal processing and…
The distributed computation of a Nash equilibrium in aggregative games is gaining increased traction in recent years. Of particular interest is the mediator-free scenario where individual players only access or observe the decisions of…
This paper is about computing constrained approximate Nash equilibria in polymatrix games, which are succinctly represented many-player games defined by an interaction graph between the players. In a recent breakthrough, Rubinstein showed…
In this paper, for solving a broad class of large-scale nonconvex and nonsmooth optimization problems, we propose a stochastic two step inertial Bregman proximal alternating linearized minimization (STiBPALM) algorithm with variance-reduced…
Recent applications that arise in machine learning have surged significant interest in solving min-max saddle point games. This problem has been extensively studied in the convex-concave regime for which a global equilibrium solution can be…
We analyze the stability of a nonlinear dynamical model describing the noncooperative strategic interactions among the agents of a finite collection of populations. Each agent selects one strategy at a time and revises it repeatedly…
We discuss the design of state-of-the-art numerical methods for molecular dynamics, focusing on the demands of soft matter simulation, where the purposes include sampling and dynamics calculations both in and out of equilibrium. We discuss…
We propose an unconstrained optimization method based on the well-known primal-dual hybrid gradient (PDHG) algorithm. We first formulate the optimality condition of the unconstrained optimization problem as a saddle point problem. We then…
The standard risk minimization paradigm of machine learning is brittle when operating in environments whose test distributions are different from the training distribution due to spurious correlations. Training on data from many…
In this work, we present a novel characterization of approximate Nash equilibria in a class of convex games over the simplex. To achieve this, we regularize the utility functions using the Shannon entropy term, connect the solutions to the…
In this paper, we study a distributed continuous-time design for aggregative games with coupled constraints in order to seek the generalized Nash equilibrium by a group of agents via simple local information exchange. To solve the problem,…
In practical applications, decision-makers with heterogeneous dynamics may be engaged in the same decision-making process. This motivates us to study distributed Nash equilibrium seeking for games in which players are mixed-order (first-…