Tail-Risk-Safe Monte Carlo Tree Search under PAC-Level Guarantees
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918117306793984 |
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| author | Zhang, Zuyuan Ghosh, Arnob Lan, Tian |
| author_facet | Zhang, Zuyuan Ghosh, Arnob Lan, Tian |
| contents | Making decisions with respect to just the expected returns in Monte Carlo Tree Search (MCTS) cannot account for the potential range of high-risk, adverse outcomes associated with a decision. To this end, safety-aware MCTS often consider some constrained variants -- by introducing some form of mean risk measures or hard cost thresholds. These approaches fail to provide rigorous tail-safety guarantees with respect to extreme or high-risk outcomes (denoted as tail-risk), potentially resulting in serious consequence in high-stake scenarios. This paper addresses the problem by developing two novel solutions. We first propose CVaR-MCTS, which embeds a coherent tail risk measure, Conditional Value-at-Risk (CVaR), into MCTS. Our CVaR-MCTS with parameter $α$ achieves explicit tail-risk control over the expected loss in the "worst $(1-α)\%$ scenarios." Second, we further address the estimation bias of tail-risk due to limited samples. We propose Wasserstein-MCTS (or W-MCTS) by introducing a first-order Wasserstein ambiguity set $\mathcal{P}_{\varepsilon_{s}}(s,a)$ with radius $\varepsilon_{s}$ to characterize the uncertainty in tail-risk estimates. We prove PAC tail-safety guarantees for both CVaR-MCTS and W-MCTS and establish their regret. Evaluations on diverse simulated environments demonstrate that our proposed methods outperform existing baselines, effectively achieving robust tail-risk guarantees with improved rewards and stability. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_05441 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Tail-Risk-Safe Monte Carlo Tree Search under PAC-Level Guarantees Zhang, Zuyuan Ghosh, Arnob Lan, Tian Machine Learning Artificial Intelligence Making decisions with respect to just the expected returns in Monte Carlo Tree Search (MCTS) cannot account for the potential range of high-risk, adverse outcomes associated with a decision. To this end, safety-aware MCTS often consider some constrained variants -- by introducing some form of mean risk measures or hard cost thresholds. These approaches fail to provide rigorous tail-safety guarantees with respect to extreme or high-risk outcomes (denoted as tail-risk), potentially resulting in serious consequence in high-stake scenarios. This paper addresses the problem by developing two novel solutions. We first propose CVaR-MCTS, which embeds a coherent tail risk measure, Conditional Value-at-Risk (CVaR), into MCTS. Our CVaR-MCTS with parameter $α$ achieves explicit tail-risk control over the expected loss in the "worst $(1-α)\%$ scenarios." Second, we further address the estimation bias of tail-risk due to limited samples. We propose Wasserstein-MCTS (or W-MCTS) by introducing a first-order Wasserstein ambiguity set $\mathcal{P}_{\varepsilon_{s}}(s,a)$ with radius $\varepsilon_{s}$ to characterize the uncertainty in tail-risk estimates. We prove PAC tail-safety guarantees for both CVaR-MCTS and W-MCTS and establish their regret. Evaluations on diverse simulated environments demonstrate that our proposed methods outperform existing baselines, effectively achieving robust tail-risk guarantees with improved rewards and stability. |
| title | Tail-Risk-Safe Monte Carlo Tree Search under PAC-Level Guarantees |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2508.05441 |