PAPAL: A Provable PArticle-based Primal-Dual ALgorithm for Mixed Nash Equilibrium

• URL: http://arxiv.org/abs/2303.00970v2
• Date: Mon, 20 Nov 2023 22:51:36 GMT
• Title: PAPAL: A Provable PArticle-based Primal-Dual ALgorithm for Mixed Nash Equilibrium
• Authors: Shihong Ding, Hanze Dong, Cong Fang, Zhouchen Lin, Tong Zhang
• Abstract summary: We consider the non-AL equilibrium nonconptotic objective function in two-player zero-sum continuous games. The proposed algorithm employs the movements of particles to represent the updates of random strategies for the $ilon$-mixed Nash equilibrium.
• Score: 62.51015395213579
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We consider the non-convex non-concave objective function in two-player zero-sum continuous games. The existence of pure Nash equilibrium requires stringent conditions, posing a major challenge for this problem. To circumvent this difficulty, we examine the problem of identifying a mixed Nash equilibrium, where strategies are randomized and characterized by probability distributions over continuous domains.To this end, we propose PArticle-based Primal-dual ALgorithm (PAPAL) tailored for a weakly entropy-regularized min-max optimization over probability distributions. This algorithm employs the stochastic movements of particles to represent the updates of random strategies for the $\epsilon$-mixed Nash equilibrium. We offer a comprehensive convergence analysis of the proposed algorithm, demonstrating its effectiveness. In contrast to prior research that attempted to update particle importance without movements, PAPAL is the first implementable particle-based algorithm accompanied by non-asymptotic quantitative convergence results, running time, and sample complexity guarantees. Our framework contributes novel insights into the particle-based algorithms for continuous min-max optimization in the general non-convex non-concave setting.

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