Characterize parameter dependence of MCTS convergence rates

Characterize the dependence of robust and non-robust Monte Carlo Tree Search convergence rates on the number of states, number of actions, and tree-search depth, including the problem-dependent factors that determine these rates.

Background

The paper proves an expected root-value convergence rate of order $\mathcal{O}(n^{-1/2})$ for the proposed robust MCTS algorithm and observes that this matches the corresponding rate for standard MCTS. However, the analysis does not provide an explicit, interpretable dependence of the convergence bounds on structural parameters such as the state-space size, action-space size, and search-tree depth. Establishing such dependence would enable meaningful comparisons with other online robust reinforcement-learning methods and clarify how the theoretical guarantees scale with problem complexity.

The conclusion explicitly identifies this gap for both robust and non-robust MCTS settings, making it an unresolved theoretical problem rather than merely an implementation aspiration.