Title: Dimension-Adaptive MCTS: Optimal Sample Complexity for Continuous Action Planning
Primary area: reinforcement learning
Keywords: Monte-Carlo Tree Search; Continuous Reinforcement Learning Planning

Abstract: We study continuous-action Monte Carlo Tree Search (MCTS) in a $d$-dimensional action space when the 
optimal action-value function $Q^*(s,\cdot)$ is $\beta$-Hölder continuous with constant~$L$. We show that a 
dimension-adaptive $\varepsilon$-net schedule combined with power-mean backups and a polynomial exploration 
bonus finds an $\varepsilon$-optimal action in  $ \tilde{O}\left(\sigma^2 L^{d/\beta} \varepsilon^{-(d/\beta+2)}\right) $
simulations, matching standard continuum-armed lower bounds up to logs while remaining practical 
via on-demand, capped random nets. We further demonstrate that our method significantly outperforms 
baseline methods on continuous control planning problems. Our work bridges the gap between theoretical 
reinforcement learning and practical planning algorithms, providing a principled approach to 
high-dimensional continuous action space exploration.