多Agent学习中的连续策略复制动力学
Continuous Strategy Replicator Dynamics for Multi--Agent Learning
摘要：
近年来，多智能体的学习和适应问题引起了人们的极大关注。有人建议，多智能体学习的动力学可以使用来自种群生物学的复制子方程来研究。到目前为止，大多数现有的研究已被限制到离散的策略空间与少数可用的行动。然而，在许多情况下，代理商可用的选择更好地表征连续光谱。本文提出了一个推广的复制框架，允许研究的自适应动态Q-学习代理与连续的战略空间。代替概率向量，代理策略现在由连续变量上的概率度量来表征。其结果是，常微分方程的离散情况下被替换为一个系统的耦合积分-微分复制方程，描述的相互演变的个人代理策略。我们推导出一组功能方程描述的稳定状态的复制动力学，检查他们的解决方案，几个两个玩家的游戏，并确认我们的分析结果，使用模拟。
英文摘要：
The problem of multi-agent learning and adaptation has attracted a great deal of attention in recent years. It has been suggested that the dynamics of multi agent learning can be studied using replicator equations from population biology. Most existing studies so far have been limited to discrete strategy spaces with a small number of available actions. In many cases, however, the choices available to agents are better characterized by continuous spectra. This paper suggests a generalization of the replicator framework that allows to study the adaptive dynamics of Q-learning agents with continuous strategy spaces. Instead of probability vectors, agents strategies are now characterized by probability measures over continuous variables. As a result, the ordinary differential equations for the discrete case are replaced by a system of coupled integral--differential replicator equations that describe the mutual evolution of individual agent strategies. We derive a set of functional equations describing the steady state of the replicator dynamics, examine their solutions for several two-player games, and confirm our analytical results using simulations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
