Bayesian Mixture Modeling and Inference based Thompson Sampling in Monte-Carlo Tree Search

Monte-Carlo tree search (MCTS) has been drawing great interest in recent years for planning and learning under uncertainty. One of the key challenges is the trade-off between exploration and exploitation. To address this, we present a novel approach for MCTS using Bayesian mixture modeling and inference based Thompson sampling and apply it to the problem of online planning in MDPs. Our algorithm, named Dirichlet-NormalGamma MCTS (DNG-MCTS), models the uncertainty of the accumulated reward for actions in the search tree as a mixture of Normal distributions. We perform inferences on the mixture in Bayesian settings by choosing conjugate priors in the form of combinations of Dirichlet and NormalGamma distributions and select the best action at each decision node using Thompson sampling. Experimental results confirm that our algorithm advances the state-of-the-art UCT approach with better values on several benchmark problems.