Tail-Risk-Safe Monte Carlo Tree Search under PAC-Level Guarantees

2025-08-07

AI Summary

To address the lack of rigorous safety guarantees against tail risk in Monte Carlo Tree Search (MCTS), this paper proposes the first safety-aware MCTS framework with provable Probably Approximately Correct (PAC) tail-risk control. Methodologically, it introduces a novel integration of Conditional Value-at-Risk (CVaR) with a Wasserstein ambiguity set to model the worst-case (1−α)% tail scenarios, embedded within a bias-corrected MCTS search mechanism that ensures theoretically grounded PAC tail-risk constraints. Crucially, the framework simultaneously optimizes expected reward while explicitly suppressing extreme adverse outcomes. Experiments across diverse high-risk simulation environments demonstrate that our approach significantly outperforms existing baselines—whether mean-risk–oriented or hard-threshold–based—achieving joint improvements in reward performance, policy stability, and tail-robustness.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Multiagent Systems: Multiagent Systems under Uncertainty
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Security and Privacy: Large-scale security measurements

Abstract

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.

Problem

• Ensures tail-risk safety in Monte Carlo Tree Search
• Addresses estimation bias in tail-risk with limited samples
• Provides PAC guarantees for robust tail-risk control

Innovation

• CVaR-MCTS for tail-risk control
• Wasserstein-MCTS reduces estimation bias
• PAC tail-safety guarantees proven