Quality-based Rewards for Monte-Carlo Tree Search Simulations

Monte-Carlo Tree Search is a best-first search technique based on simulations to sample the state space of a decision-making problem. In games, positions are evaluated based on estimates obtained from rewards of numerous randomized play-outs. Generally, rewards from play-outs are discrete values representing the outcome of the game (loss, draw, or win), e.g., r ∈ {−1, 0, 1}, which are backpropagated from expanded leaf nodes to the root node. However, a play-out may provide additional information. In this paper, we introduce new measures for assessing the a posteriori quality of a simulation. We show that altering the rewards of play-outs based on their assessed quality improves results in six distinct two-player games and in the General Game Playing agent CADIAPLAYER. We propose two specific enhancements, the Relative Bonus and Qualitative Bonus. Both are used as control variates, a variance reduction method for statistical simulation. Relative Bonus is based on the number of moves made during a simulation and Qualitative Bonus relies on a domain-dependent assessment of the game’s terminal state. We show that the proposed enhancements, both separate and combined, lead to significant performance increases in the domains discussed.