Monte Carlo Tree Search (MCTS) algorithms such as AlphaGo and MuZero have achieved superhuman performance in many challenging tasks. However, the computational complexity of MCTS-based algorithms is influenced by the size of the search space. To address this issue, we propose a novel probability tree state abstraction (PTSA) algorithm to improve the search efficiency of MCTS. A general tree state abstraction with path transitivity is defined. In addition, the probability tree state abstraction is proposed for fewer mistakes during the aggregation step. Furthermore, the theoretical guarantees of the transitivity and aggregation error bound are justified. To evaluate the effectiveness of the PTSA algorithm, we integrate it with state-of-the-art MCTS-based algorithms, such as Sampled MuZero and Gumbel MuZero. Experimental results on different tasks demonstrate that our method can accelerate the training process of state-of-the-art algorithms with 10%-45% search space reduction.

翻译：蒙特卡洛树搜索 (MCTS) 算法（如AlphaGo和MuZero）已在诸多具有挑战性的任务中展现出超人般的性能。然而，基于MCTS的算法其计算复杂度受搜索空间大小的影响。为解决这一问题，我们提出一种新颖的概率树状态抽象 (PTSA) 算法，旨在提升MCTS的搜索效率。我们定义了具有路径传递性的一般树状态抽象。此外，提出概率树状态抽象以减少聚合步骤中的错误。同时，论证了传递性与聚合误差界的理论保证。为评估PTSA算法的有效性，我们将其与现有最优的基于MCTS的算法（如Sampled MuZero和Gumbel MuZero）集成。在不同任务上的实验结果表明，我们的方法能够将现有最优算法的训练过程加速10%-45%的搜索空间缩减。