为连续时间平均场博弈设计最优粗相关均衡，实现性能优化与可学习性。
Optimal Coarse Correlated Equilibria in Mean Field Games: Linear Programming and No-Regret Learning
- 通过线性规划构建最优粗相关均衡的数学框架
- 提出无后悔学习算法并给出明确收敛速率
- 适合研究博弈优化与大规模系统协调的学者
我们引入了连续时间平均场博弈中的最优粗相关均衡。粗相关均衡是一种随机推荐机制，任何个体若无视推荐而改用其他策略均无法获益。问题核心在于：在所有平均场粗相关均衡中，选择一个能优化特定性能指标的均衡，该指标可不同于代表性玩家的目标。我们建立了线性规划（LP）形式化模型，证明了最优LP粗相关均衡的存在性，并将该LP刻画与原始概率设定相联系。基于此，我们设计了一种基于等价拉格朗日形式的无后悔原对偶算法，用于学习此类均衡。我们给出了该学习算法的显式收敛速率，并通过数值例子验证方法有效性。
原文摘要 · Abstract (English)
We introduce optimal coarse correlated equilibria for continuous-time mean field games. A coarse correlated equilibrium is a randomized recommendation scheme from which no player can gain by ignoring the recommendation and switching to an alternative strategy. The problem is as follows: a moderator selects, among all mean-field coarse correlated equilibria, one that optimizes a prescribed performance criterion, which may differ from the representative player's objective. After formulating the problem, we develop a linear programming (LP) formulation, prove the existence of optimal LP coarse correlated equilibria, and relate the LP characterization to the original probabilistic setting. Building on this characterization, we design a no-regret primal-dual algorithm, based on an equivalent Lagrangian formulation of the external-regret constraint, for learning such equilibria. We provide explicit convergence rates for the learning algorithm, and numerical examples illustrate the method.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。