通过随机游戏以最佳方式达到目标
Reaching Your Goal Optimally by Playing at Random
摘要：
最短路径博弈是两人零和博弈，在一个具有整数权重的图上进行。一个玩家，我们称之为Min，希望在最小化总重量的同时达到一组目标状态，另一个玩家则有一个对抗性的目标。这种定性可达性目标和定量总收益目标的组合是最简单的设置之一，其中Min需要记忆（权重中的伪多项式）以进行最佳播放。在这篇文章中，我们的目标是研究一个折衷方案，允许Min随机播放，但不使用内存。我们表明，在这两种情况下，最小可以达到相同的最优值。特别是，我们计算一个随机无记忆的$\varepsilon$最优策略时，它存在，概率参数化的$\varepsilon$。然后，我们将在多项式时间内确定一类允许最优随机无记忆策略的游戏。
英文摘要：
Shortest-path games are two-player zero-sum games played on a graph equipped with integer weights. One player, that we call Min, wants to reach a target set of states while minimising the total weight, and the other one has an antagonistic objective. This combination of a qualitative reachability objective and a quantitative total-payoff objective is one of the simplest setting where Min needs memory (pseudo-polynomial in the weights) to play optimally. In this article, we aim at studying a tradeoff allowing Min to play at random, but using no memory. We show that Min can achieve the same optimal value in both cases. In particular, we compute a randomised memoryless $\varepsilon$-optimal strategy when it exists, where probabilities are parametrised by $\varepsilon$. We then characterise, and decide in polynomial time, the class of games admitting an optimal randomised memoryless strategy.
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。
