Extreme Value Monte Carlo Tree Search for Classical Planning

Despite being successful in board games and reinforcement learning (RL), Monte Carlo Tree Search (MCTS) combined with Multi Armed Bandit (MAB) has seen limited success in domain-independent classical planning until recently. Previous work (Wissow and Asai, 2024) showed that UCB1, designed for bounded rewards, does not perform well as applied to cost-to-go estimates in classical planning, because cost-to-go estimates are unbounded, and showed improved performance using a Gaussian reward MAB instead. This paper further sharpens our understanding of ideal bandits for planning tasks. Existing work has two issues: first, Gaussian MABs under-specify the support of cost-to-go estimates as (-∞, ∞), which we can narrow down. Second, Full Bellman backup (Schulte and Keller, 2014) that backpropagates sample max/min lacks theoretical justification. We use Peaks-Over-Threashold Extreme Value Theory to resolve both issues at once, propose a new bandit algorithm (UCB1-Uniform). We formally prove its regret bound and empirically demonstrate its performance in classical planning.