Multi-agent path finding (MAPF) is a classical NP-hard problem that considers planning collision-free paths for multiple agents simultaneously. A MAPF problem is typically solved via addressing a sequence of single-agent path finding subproblems in which well-studied algorithms such as are applicable. Existing methods based on this idea, however, rely on an exhaustive search and therefore only have asymptotic performance guarantees. In this article, we provide a modeling paradigm that converts a MAPF problem into a stochastic process and adopts a confidence bound based rule for finding the optimal state transition strategy. A randomized algorithm is proposed to solve this stochastic process, which combines ideas from conflict based search and Monte Carlo tree search. We show that the proposed method is almost surely optimal while enjoying non-asymptotic performance guarantees. In particular, the proposed method can, after solving single-agent subproblems, produce a feasible solution with suboptimality bounded by . The theoretical results are verified by several numerical experiments based on grid maps.

中文翻译：

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具有非渐近性能保证的多智能体路径查找的随机过程方法

多智能体寻路（MAPF）是一个经典的 NP 难题，考虑同时为多个智能体规划无碰撞路径。MAPF 问题通常通过解决一系列单智能体寻路子问题来解决，其中可以应用经过充分研究的算法。然而，基于这种想法的现有方法依赖于穷举搜索，因此仅具有渐近性能保证。在本文中，我们提供了一种建模范例，将 MAPF 问题转换为随机过程，并采用基于置信界限的规则来寻找最佳状态转换策略。提出了一种随机算法来解决这个随机过程，该算法结合了基于冲突的搜索和蒙特卡罗树搜索的思想。我们证明所提出的方法几乎肯定是最优的，同时享有非渐近性能保证。特别是，所提出的方法可以在解决单智能体子问题后，产生一个以 为界的次优可行解。通过基于网格图的多次数值实验验证了理论结果。