arXiv:2610.05516 · v2

Distributed Learning of $α$-Potential Functions in Strategic Multi-agent Systems

首次提交 2026-10-05 04:33

版本更新 2026-11-08 09:14

雷达观测 2026-11-10 12:16

摘要

We study the problem of computing the tightest $α$-potential approximation of a general-sum game over continuous action spaces, within a prescribed class of potential functions and when each player has access only to its own utility function. The difficulty is twofold: the approximation error involves a worst-case search over an infinite set of unilateral deviations, and the required utility information is distributed across players. For a linear-in-parameters potential class, we use an exact finite-tuple reformulation that separates the problem into a global outer search over deviation tuples and distributed convex inner problems. We develop a primal--dual inner oracle tailored to this structure and establish a uniform one-sided accuracy guarantee. This oracle can be combined with global outer search to obtain an end-to-end guarantee on the outer optimization error. We also develop a projected zeroth-order outer method as a computationally lighter alternative for higher-dimensional problems. Numerical experiments illustrate the accuracy--computation tradeoff between the two outer-search methods and show that the proposed optimization framework can improve upon analytical $α$-potential constructions.

作者备注：15 pages, 4 figures