Truncated Noisy Best-Response Algorithms: Toward Game Theoretic Learning with Safety Guarantees

2026-09-10

AI Summary

研究通过提出截断噪声最佳响应算法解决多智能体协调问题，确保在子模最大化目标下达到安全与性能的平衡。

Abstract

We consider a game theoretic approach to solve multi-agent coordination problems with submodular maximization objectives. It is known for such problems that the Nash equilibria for the corresponding game are always within 50% of the optimal, but that the equilibria which achieve this worst-case bound are not stable. To exploit this instability, we propose a family of algorithms which we call Truncated Noisy Best-Response (TNBR) Algorithms. These algorithms are flexibly characterized by agents asynchronously and stochastically selecting actions from a neighbourhood of their best response payoffs. We compute bounds on the recurrent classes of TNBR algorithms' associated Markov chains. Our bounds fall into two categories: first, "Performance" bounds ensure that TNBR algorithms always have a high-value recurrent state; second, "Safety" bounds ensure that TNBR algorithms never have arbitrarily-bad recurrent states. Furthermore, these two types of bounds are linked by a waterbed-like effect: every game with a poor Safety guarantee necessarily has a favorable Performance guarantee.

Problem

• Multi-agent Coordination
• Submodular Maximization
• Nash Equilibria
• Safety Guarantees
• Performance

Innovation

• Truncated Noisy Best-Response (TNBR)
• submodular maximization
• game theoretic learning
• Safety Guarantees
• Performance Bounds