Power Mean Estimation in Stochastic Continuous Monte-Carlo Tree Search

Tuan Quang Dam
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:12344-12376, 2025.

Abstract

Monte Carlo Tree Search (MCTS) has demonstrated success in online planning for deterministic environments, yet significant challenges remain in adapting it to stochastic Markov Decision Processes (MDPs), particularly in continuous state-action spaces. Existing methods, such as HOOT, which combines MCTS with the Hierarchical Optimistic Optimization (HOO) bandit strategy, address continuous spaces but rely on a logarithmic exploration bonus that lacks theoretical guarantees in non-stationary, stochastic settings. Recent advancements, such as POLY-HOOT, introduced a polynomial bonus term to achieve convergence in deterministic MDPs, though a similar theory for stochastic MDPs remains undeveloped. In this paper, we propose a novel MCTS algorithm, Stochastic-Power-HOOT, designed for continuous, stochastic MDPs. Stochastic-Power-HOOT integrates a power mean as a value backup operator, alongside a polynomial exploration bonus to address the non-stationarity inherent in continuous action spaces. Our theoretical analysis establishes that Stochastic-Power-HOOT converges at a polynomial rate of $\mathcal{O}(n^{-\zeta})$, $\zeta \in (0,1/2)$, where $ n $ is the number of visited trajectories, thereby extending the non-asymptotic convergence guarantees of POLY-HOOT to stochastic environments. Experimental results on stochastic tasks validate our theoretical findings, demonstrating the effectiveness of Stochastic-Power-HOOT in continuous, stochastic domains.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-dam25b, title = {Power Mean Estimation in Stochastic Continuous {M}onte-{C}arlo Tree Search}, author = {Dam, Tuan Quang}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {12344--12376}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/dam25b/dam25b.pdf}, url = {https://proceedings.mlr.press/v267/dam25b.html}, abstract = {Monte Carlo Tree Search (MCTS) has demonstrated success in online planning for deterministic environments, yet significant challenges remain in adapting it to stochastic Markov Decision Processes (MDPs), particularly in continuous state-action spaces. Existing methods, such as HOOT, which combines MCTS with the Hierarchical Optimistic Optimization (HOO) bandit strategy, address continuous spaces but rely on a logarithmic exploration bonus that lacks theoretical guarantees in non-stationary, stochastic settings. Recent advancements, such as POLY-HOOT, introduced a polynomial bonus term to achieve convergence in deterministic MDPs, though a similar theory for stochastic MDPs remains undeveloped. In this paper, we propose a novel MCTS algorithm, Stochastic-Power-HOOT, designed for continuous, stochastic MDPs. Stochastic-Power-HOOT integrates a power mean as a value backup operator, alongside a polynomial exploration bonus to address the non-stationarity inherent in continuous action spaces. Our theoretical analysis establishes that Stochastic-Power-HOOT converges at a polynomial rate of $\mathcal{O}(n^{-\zeta})$, $\zeta \in (0,1/2)$, where $ n $ is the number of visited trajectories, thereby extending the non-asymptotic convergence guarantees of POLY-HOOT to stochastic environments. Experimental results on stochastic tasks validate our theoretical findings, demonstrating the effectiveness of Stochastic-Power-HOOT in continuous, stochastic domains.} }
Endnote
%0 Conference Paper %T Power Mean Estimation in Stochastic Continuous Monte-Carlo Tree Search %A Tuan Quang Dam %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-dam25b %I PMLR %P 12344--12376 %U https://proceedings.mlr.press/v267/dam25b.html %V 267 %X Monte Carlo Tree Search (MCTS) has demonstrated success in online planning for deterministic environments, yet significant challenges remain in adapting it to stochastic Markov Decision Processes (MDPs), particularly in continuous state-action spaces. Existing methods, such as HOOT, which combines MCTS with the Hierarchical Optimistic Optimization (HOO) bandit strategy, address continuous spaces but rely on a logarithmic exploration bonus that lacks theoretical guarantees in non-stationary, stochastic settings. Recent advancements, such as POLY-HOOT, introduced a polynomial bonus term to achieve convergence in deterministic MDPs, though a similar theory for stochastic MDPs remains undeveloped. In this paper, we propose a novel MCTS algorithm, Stochastic-Power-HOOT, designed for continuous, stochastic MDPs. Stochastic-Power-HOOT integrates a power mean as a value backup operator, alongside a polynomial exploration bonus to address the non-stationarity inherent in continuous action spaces. Our theoretical analysis establishes that Stochastic-Power-HOOT converges at a polynomial rate of $\mathcal{O}(n^{-\zeta})$, $\zeta \in (0,1/2)$, where $ n $ is the number of visited trajectories, thereby extending the non-asymptotic convergence guarantees of POLY-HOOT to stochastic environments. Experimental results on stochastic tasks validate our theoretical findings, demonstrating the effectiveness of Stochastic-Power-HOOT in continuous, stochastic domains.
APA
Dam, T.Q.. (2025). Power Mean Estimation in Stochastic Continuous Monte-Carlo Tree Search. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:12344-12376 Available from https://proceedings.mlr.press/v267/dam25b.html.

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