Distributed Algorithms for $\alpha$-Potential Functions in General-Sum Games

2026-10-04

AI Summary

This study addresses the challenge of infinite deviation search in computing α-potential approximations for general-sum games with continuous action spaces. To overcome this, we propose a decoupled architecture based on finite-tuple reconstruction. Methodologically, global search is decoupled from distributed convex optimization by designing a primal-dual inner oracle and a projected zeroth-order outer algorithm, which computes the tightest α-potential approximation within linearly parameterized potential classes. This framework establishes unified accuracy guarantees while enabling efficient distributed computation. Numerical experiments demonstrate an effective trade-off between approximation precision and computational overhead, showing that the proposed approach significantly outperforms conventional analytical construction methods.

Abstract

We study the problem of computing the tightest \(\alpha\)-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 \(\alpha\)-potential constructions.

Problem

• general-sum games
• potential approximation
• continuous action spaces
• distributed information
• worst-case deviation

Innovation

• alpha-potential approximation
• distributed optimization
• primal-dual oracle
• zeroth-order method
• general-sum games