UCT, a state-of-the art algorithm for Monte Carlo tree search (MCTS) in games and Markov decision processes, is based on UCB, a sampling policy for the Multi-armed Bandit problem (MAB) that minimizes the cumulative regret. However, search differs from MAB in that in MCTS it is usually only the final "arm pull" (the actual move selection) that collects a reward, rather than all "arm pulls". Therefore, it makes more sense to minimize the simple regret, as opposed to the cumulative regret. We begin by introducing policies for multi-armed bandits with lower finite-time and asymptotic simple regret than UCB, using it to develop a two-stage scheme (SR+CR) for MCTS which outperforms UCT empirically. Optimizing the sampling process is itself a metareasoning problem, a solution of which can use value of information (VOI) techniques. Although the theory of VOI for search exists, applying it to MCTS is non-trivial, as typical myopic assumptions fail. Lacking a complete working VOI theory for MCTS, we nevertheless propose a sampling scheme that is "aware" of VOI, achieving an algorithm that in empirical evaluation outperforms both UCT and the other proposed algorithms.
The UCT algorithm, an extension of UCB to Monte-Carlo Tree Search is described in @cite_1 , and shown to outperform many state of the art search algorithms in both MDP and adversarial games @cite_5 @cite_3 .
@cite_5 @cite_1 @cite_3
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Monte-Carlo Tree Search (MCTS) is a successful approach for improving the performance of game-playing programs. This paper presents the Accelerated UCT algorithm, which overcomes a weakness of MCTS caused by deceptive structures which often appear in game tree search. It consists in using a new backup operator that assigns higher weights to recently visited actions, and lower weights to actions that have not been visited for a long time. Results in Othello, Havannah, and Go show that Accelerated UCT is not only more effective than previous approaches but also improves the strength of Fuego, which is one of the best computer Go programs. Monte Carlo tree search (MCTS) has been recently very successful for game playing, particularly for games where the evaluation of a state is difficult to compute, such as Go or General Games. We compare nested Monte Carlo (NMC) search, upper confidence bounds for trees (UCT-T), UCT with transposition tables (UCT+T), and a simple combination of NMC and UCT+T (MAX) on single-player games of the past General Game Playing (GGP) competitions. We show that transposition tables improve UCT and that MAX is the best of these four algorithms. Using UCT+T, the program Ary won the 2009 GGP competition. MAX and NMC are slight improvements over this 2009 version. Monte-Carlo Tree Search (MCTS) is remarkably successful in two-player games, but parallelizing MCTS has been notoriously difficult to scale well, especially in distributed environments. For a distributed parallel search, transposition-table driven scheduling (TDS) is known to be efficient in several domains. We present a massively parallel MCTS algorithm, that applies the TDS parallelism to the Upper Confidence bound Applied to Trees (UCT) algorithm, which is the most representative MCTS algorithm. To drastically decrease communication overhead, we introduce a reformulation of UCT called Depth-First UCT. The parallel performance of the algorithm is evaluated on clusters using up to 1,200 cores in artificial game-trees. We show that this approach scales well, achieving 740-fold speedups in the best case. Monte-Carlo search has been successful in many non-deterministic games, and recently in deterministic games with high branching factor. One of the drawbacks of the current approaches is that even if the iterative process would last for a very long time, the selected move does not necessarily converge to a game-theoretic optimal one. In this paper we introduce a new algorithm, UCT, which extends a bandit algorithm for Monte-Carlo search. It is proven that the probability that the algorithm selects the correct move converges to 1. Moreover it is shown empirically that the algorithm converges rather fast even in comparison with alpha-beta search. Experiments in Amazons and Clobber indicate that the UCT algorithm outperforms considerably a plain Monte-Carlo version, and it is competitive against alpha-beta based game programs.