优化和学习纳什均衡的一般框架

Di Zhang, Wei Gu, Qing Jin
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引用次数: 0

摘要

现实生活中纳什均衡应用的关键之一是校准博弈者的成本函数。为了充分利用神经网络的近似能力,我们提出了一个利用神经网络估计博弈者成本函数的纳什均衡优化和学习通用框架。根据数据的可得性,我们提出了两种方法:(a)两阶段方法:我们需要棋手策略和相关函数值的数据对,先用单调神经网络或图神经网络学习棋手的成本函数,然后用学习到的神经网络求解纳什均衡;(b)联合方法:我们使用均衡的部分真实观测数据和上下文信息(如天气),同时优化和学习纳什均衡。该问题被表述为带有均衡约束条件的优化问题,并使用改进的后向传播算法求解。所提出的方法在数值实验中得到了验证。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A General Framework for Optimizing and Learning Nash Equilibrium
One key in real-life Nash equilibrium applications is to calibrate players' cost functions. To leverage the approximation ability of neural networks, we proposed a general framework for optimizing and learning Nash equilibrium using neural networks to estimate players' cost functions. Depending on the availability of data, we propose two approaches (a) the two-stage approach: we need the data pair of players' strategy and relevant function value to first learn the players' cost functions by monotonic neural networks or graph neural networks, and then solve the Nash equilibrium with the learned neural networks; (b) the joint approach: we use the data of partial true observation of the equilibrium and contextual information (e.g., weather) to optimize and learn Nash equilibrium simultaneously. The problem is formulated as an optimization problem with equilibrium constraints and solved using a modified Backpropagation Algorithm. The proposed methods are validated in numerical experiments.
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