Extreme Value Monte Carlo Tree Search (Extended Abstract)

Monte-Carlo Tree Search (MCTS) combined with Multi-Armed Bandit (MAB) has had limited success in domain-independent classical planning until recently. Previous work (Wissow and Asai 2023) showed that UCB1, designed for bounded rewards, does not perform well when applied to the cost-to-go estimates of classical planning, which are unbounded in R, then improved the performance by using a Gaussian reward MAB instead. We further sharpen our understanding of ideal bandits for planning tasks by resolving three issues: First, Gaussian MABs under-specify the support of cost-to-go estimates as −∞, ∞. Second, Full-Bellman backup that backpropagates max/min of samples lacks theoretical justifications. Third, removing dead-ends lacks justifications in Monte-Carlo backup. We use Extreme Value Theory Type 2 to resolve them at once, propose two bandits (UCB1-Uniform/Power), and apply them to MCTS for classical planning. We formally prove their regret bounds and empirically demonstrate their performance in classical planning.