Scalable Robust MCTS with Anytime Deterministic Optimality Guarantees

Tomer Massas, Vadim Indelman

MDP planners often rely on nominal transition models that may differ from the true dynamics. Robust MDP planning accounts for this uncertainty through a set of admissible models, but doing so with limited online computation is challenging: the search tree grows exponentially with the horizon and each robust backup requires an additional optimization. Existing online robust methods remain limited in scale and offer at most probabilistic guarantees. We introduce, to the best of our knowledge, the first deterministic anytime guarantees for robust online MDP planning. We restrict computation to the sampled search tree while deterministically bounding the contribution of unsampled trajectories. For any fixed policy, we derive lower and upper bounds on the gap between its projected and true robust values under rectangular and non-rectangular uncertainty sets. Under rectangular uncertainty, we propagate these bounds through the robust Bellman operator to bound the optimal robust value. These bounds are computable from the current sampled tree, hold at every node, tighten as the sampled support expands, and converge to the robust values as full support is recovered. We develop CAR-MCTS,…