全切换策略改进的复杂性
The Complexity of All-switches Strategy Improvement
AI总结：
该论文证明了全切换策略改进算法在奇偶博弈、平均收益博弈、折扣收益博弈和简单随机博弈中的边切换问题与最优策略问题均为PSPACE完全问题，并扩展至立方体上的底部-对映算法。
摘要：
策略改进是一类广泛使用且被深入研究的算法，用于求解基于图的无限博弈。这些算法由切换规则参数化，其中最自然的规则之一是“全切换”，即在每次迭代中尽可能多地切换边。延续最近的一系列工作，我们从计算复杂性的角度研究全切换策略改进。我们考虑两个自然的决策问题，两者的输入都是一个博弈$G$、一个初始策略$s$和一条边$e$。这两个问题是：1.) 边切换问题，即当从$s$开始对博弈$G$运行全切换策略改进时，边$e$是否曾被切换？2.) 最优策略问题，即当从$s$开始对博弈$G$运行策略改进时，边$e$是否被用于最终找到的策略中？我们证明了在以下设置中，边切换问题和最优策略问题是$\mathtt{PSPACE}$完全的：使用Vöge和Jurdziński的离散策略改进算法的奇偶博弈；使用增益-偏差算法[14,37]的平均收益博弈；以及使用其标准策略改进算法的折扣收益博弈和简单随机博弈。我们还证明了在立方体上寻找无环唯一汇点方向的底部-对映算法中，与边切换类似的问题也是$\mathtt{PSPACE}$完全的。
英文摘要：
Strategy improvement is a widely-used and well-studied class of algorithms for solving graph-based infinite games. These algorithms are parameterized by a switching rule, and one of the most natural rules is "all switches" which switches as many edges as possible in each iteration. Continuing a recent line of work, we study all-switches strategy improvement from the perspective of computational complexity. We consider two natural decision problems, both of which have as input a game $G$, a starting strategy $s$, and an edge $e$. The problems are: 1.) The edge switch problem, namely, is the edge $e$ ever switched by all-switches strategy improvement when it is started from $s$ on game $G$? 2.) The optimal strategy problem, namely, is the edge $e$ used in the final strategy that is found by strategy improvement when it is started from $s$ on game $G$? We show $\mathtt{PSPACE}$-completeness of the edge switch problem and optimal strategy problem for the following settings: Parity games with the discrete strategy improvement algorithm of Vöge and Jurdziński; mean-payoff games with the gain-bias algorithm [14,37]; and discounted-payoff games and simple stochastic games with their standard strategy improvement algorithms. We also show $\mathtt{PSPACE}$-completeness of an analogous problem to edge switch for the bottom-antipodal algorithm for finding the sink of an Acyclic Unique Sink Orientation on a cube.
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。
