Beam Monte-Carlo Tree Search

Monte-Carlo Tree Search (MCTS) is a state-of-the-art stochastic search algorithm that has successfully been applied to various multi- and one-player games (puzzles). Beam search is a search method that only expands a limited number of promising nodes per tree level, thus restricting the space complexity of the underlying search algorithm to linear in the tree depth. This paper presents Beam Monte-Carlo Tree Search (BMCTS), combining the ideas of MCTS and beam search. Like MCTS, BMCTS builds a search tree using Monte-Carlo simulations as state evaluations. When a predetermined number of simulations has traversed the nodes of a given tree depth, these nodes are sorted by their estimated value, and only a fixed number of them is selected for further exploration. In our experiments with the puzzles SameGame, Clickomania and Bubble Breaker, BMCTS significantly outperforms MCTS at equal time controls. We show that the improvement is equivalent to an up to four-fold increase in computing time for MCTS.