一般和博弈中 $\alpha$-势函数的分布式算法
Distributed Algorithms for $α$-Potential Functions in General-Sum Games
- Johns Hopkins University（约翰斯·霍普金斯大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
针对连续动作空间的一般和博弈，提出分布式算法计算最紧α-势近似，通过有限元组重构和原始-对偶预言机实现端到端保证，并验证了精度-计算权衡。
AI中文摘要：
我们研究了在连续动作空间上，在给定的一类势函数中，且每个玩家只能访问自身效用函数的情况下，计算一般和博弈的最紧 $\alpha$-势近似的问题。难点有两方面：近似误差涉及对无限单边偏离集合的最坏情况搜索，且所需的效用信息分布在各个玩家之间。对于线性参数势函数类，我们使用一种精确的有限元组重构，将问题分解为对偏离元组的全局外部搜索和分布式凸内部问题。我们开发了一种针对该结构定制的原始-对偶内部预言机，并建立了均匀的单侧精度保证。该预言机可与全局外部搜索结合，以获得外部优化误差的端到端保证。我们还开发了一种投影零阶外部方法，作为高维问题计算上更轻量的替代方案。数值实验展示了两种外部搜索方法在精度-计算之间的权衡，并表明所提出的优化框架可以改进解析 $\alpha$-势构造。
英文摘要：
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.
