可拓形式博弈平滑的理论与实践进展
Theoretical and Practical Advances on Smoothing for Extensive-Form Games
摘要：
稀疏迭代法，特别是一阶方法，被认为是解决大规模两人零和扩展形式博弈最有效的方法之一。这些方法的收敛速度在很大程度上取决于距离生成函数的性质，他们是basedon. We调查的加速一阶方法解决扩展形式的游戏通过更好的设计的扩张熵函数-一类距离生成函数相关的域与扩展形式的游戏。通过引入一个新的加权方案的扩张熵函数，我们开发的第一个距离生成函数的战略空间的序列游戏，没有依赖于分支因子的球员。这一结果提高了收敛速度的几个一阶方法的一个因素的$Ω(b^dd)$，其中$b$是分支因子的球员，和$d$是深度的游戏树。到目前为止，反事实遗憾最小化方法在实践中更快，更受欢迎，比一阶方法，尽管他们的理论上的收敛速度较低。使用我们的新的加权方案和实际调整，我们表明，第一次，过度的差距技术可以更快地比最快的反事实遗憾最小化算法，CFR+，在实践中。
英文摘要：
Sparse iterative methods, in particular first-order methods, are known to be among the most effective in solving large-scale two-player zero-sum extensive-form games. The convergence rates of these methods depend heavily on the properties of the distance-generating function that they are based on. We investigate the acceleration of first-order methods for solving extensive-form games through better design of the dilated entropy function---a class of distance-generating functions related to the domains associated with the extensive-form games. By introducing a new weighting scheme for the dilated entropy function, we develop the first distance-generating function for the strategy spaces of sequential games that has no dependence on the branching factor of the player. This result improves the convergence rate of several first-order methods by a factor of $Ω(b^dd)$, where $b$ is the branching factor of the player, and $d$ is the depth of the game tree. Thus far, counterfactual regret minimization methods have been faster in practice, and more popular, than first-order methods despite their theoretically inferior convergence rates. Using our new weighting scheme and practical tuning we show that, for the first time, the excessive gap technique can be made faster than the fastest counterfactual regret minimization algorithm, CFR+, in practice.
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。
