Learning in Games via Reinforcement and Regularization
研究一类强化学习动态，其中玩家根据累积收益减去正则项调整混合策略，扩展了指数学习的性质，包括消除劣势策略、严格纳什均衡的渐近稳定性以及零和博弈中时间平均轨迹的收敛。
We investigate a class of reinforcement learning dynamics where players adjust their strategies based on their actions’ cumulative payoffs over time—specifically, by playing mixed strategies that maximize their expected cumulative payoff minus a regularization term. A widely studied example is exponential reinforcement learning, a process induced by an entropic regularization term which leads mixed strategies to evolve according to the replicator dynamics. However, in contrast to the class of regularization functions used to define smooth best responses in models of stochastic fictitious play, the functions used in this paper need not be infinitely steep at the boundary of the simplex; in fact, dropping this requirement gives rise to an important dichotomy between steep and nonsteep cases. In this general framework, we extend several properties of exponential learning, including the elimination of dominated strategies, the asymptotic stability of strict Nash equilibria, and the convergence of time-averaged trajectories in zero-sum games with an interior Nash equilibrium.