Finite-Time Analysis of MCTS in Continuous POMDP Planning

2026-05-08

AI Summary

This work addresses the lack of finite-time theoretical guarantees for Monte Carlo tree search (MCTS) in partially observable Markov decision processes (POMDPs) with continuous observation spaces. To this end, the authors propose Voro-POMCPOW, an algorithm that extends the UCB exploration mechanism and introduces an adaptive observation-space partitioning framework based on Voronoi cells. This approach effectively handles action-selection dependencies and non-stationarity while preserving the original observation generator and maintaining a finite branching factor. The paper provides the first finite-time theoretical analysis for MCTS in continuous POMDPs, establishing high-probability polynomial concentration bounds on root-node value estimates and finite-time bounds on partitioning error. Empirical results demonstrate that Voro-POMCPOW achieves competitive performance while offering strong theoretical guarantees and is readily extensible to continuous MDPs.

Abstract

This paper presents a finite-time analysis for Monte Carlo Tree Search (MCTS) in Partially Observable Markov Decision Processes (POMDPs), with probabilistic concentration bounds in both discrete and continuous observation spaces. While MCTS-style solvers such as POMCP achieve empirical success in many applications, rigorous finite-time guarantees remain an open problem due to the nonstationarity and the interdependencies induced by heuristic action selection (e.g., UCB). In the discrete setting, we address these challenges by extending the polynomial exploration bonus to UCB in POMDP setting, yielding polynomial concentration bounds for the empirical value estimation at the root node. For continuous observation spaces, we introduce an abstract partitioning framework and propose a finite-time bound on partitioning loss. Under mild conditions, we prove highprobability bound on value estimates in POMDPs with continuous observation space. Specifically, we propose Voro-POMCPOW, a variant of POMCPOW with f inite-time guarantees that adaptively partitions the continuous observation space using Voronoi cells. This approach maintains a finite branching factor while preserving the original observation generator. Empirical validation demonstrates that the proposed Voro-POMCPOW shows competitive performance while providing theoretical guarantees. Although our analysis focuses on continuous POMDPs, the techniques developed herein are also applicable to continuous MDPs, closing another gap on the MDP side.

Problem

• MCTS
• POMDP
• finite-time analysis
• continuous observation space
• theoretical guarantees

Innovation

• Monte Carlo Tree Search
• Partially Observable Markov Decision Processes
• finite-time analysis
• Voronoi partitioning
• concentration bounds