An Efficient Algorithm for Thresholding Monte Carlo Tree Search

arXiv:2601.22600v1 Announce Type: new
Abstract: We introduce the Thresholding Monte Carlo Tree Search problem, in which, given a tree $mathcal{T}$ and a threshold $theta$, a player must answer whether the root node value of $mathcal{T}$ is at least $theta$ or not. In the given tree, `MAX’ or `MIN’ is labeled on each internal node, and the value of a `MAX’-labeled (`MIN’-labeled) internal node is the maximum (minimum) of its child values. The value of a leaf node is the mean reward of an unknown distribution, from which the player can sample rewards. For this problem, we develop a $delta$-correct sequential sampling algorithm based on the Track-and-Stop strategy that has asymptotically optimal sample complexity. We show that a ratio-based modification of the D-Tracking arm-pulling strategy leads to a substantial improvement in empirical sample complexity, as well as reducing the per-round computational cost from linear to logarithmic in the number of arms.