Softmax policy gradient is a popular algorithm for policy optimization in single-agent reinforcement learning, particularly since projection is not needed for each gradient update. However, in multi-agent systems, the lack of central coordination introduces significant additional difficulties in the convergence analysis. Even for a stochastic game with identical interest, there can be multiple Nash Equilibria (NEs), which disables proof techniques that rely on the existence of a unique global optimum. Moreover, the softmax parameterization introduces non-NE policies with zero gradient, making it difficult for gradient-based algorithms in seeking NEs. In this paper, we study the finite time convergence of decentralized softmax gradient play in a special form of game, Markov Potential Games (MPGs), which includes the identical interest game as a special case. We investigate both gradient play and natural gradient play, with and without $\log$-barrier regularization. The established convergence rates for the unregularized cases contain a trajectory-dependent constant that can be arbitrarily large, whereas the $\log$-barrier regularization overcomes this drawback, with the cost of slightly worse dependence on other factors such as the action set size. An empirical study on an identical interest matrix game confirms the theoretical findings.

翻译：软负政策梯度是单剂加固学习中政策优化的流行算法,特别是因为每个梯度更新都不需要预测。然而,在多试剂系统中,中央协调的缺乏在趋同分析中带来了更多的重大困难。即使具有相同兴趣的随机游戏,也可能存在多重Nash Equimax 政策梯度(Nes),它使依赖独特全球最佳的校准技术无法发挥作用。此外,软负负参数化引入了零梯度的非NE政策,使基于梯度的算法难以寻找NE。在本文中,我们研究了分散式软模度梯度游戏(Markov Poorlar Play)在一定时间上的趋同,其中包括相同的利息游戏(MPGs),这是一个特殊案例。我们调查了梯度游戏和自然梯度游戏(NES),而没有使用美元和美元屏障规范。非常规化案例的既定趋同率包含一个可以任意很大的轨迹常态,而基于梯度的运算法规范则克服了这一倒退。我们研究了对类似游戏的模型模型的利差研究。