Pruning game tree by rollouts

Abstract

In this paper we show that the α-β algorithm and its successor MT-SSS∗ as two classic minimax search algorithms, can be implemented as rollout algorithms, a generic algorithmic paradigm widely used in many domains. Specifically, we define a family of rollout algorithms, in which the rollout policy is restricted to select successor nodes only from a subset of the children list. We show that any rollout policy in this family (either deterministic or randomized) is guaranteed to evaluate the game tree correctly with a finite number of rollouts. Moreover, we identify simple rollout policies in this family that "implement" α-β and MT-SSS∗ Specifically, given any game tree, the rollout algorithms with these particular policies always visit the same set of leaf nodes in the same order with α-β and MT-SSS∗ respectively. Our results suggest that traditional pruning techniques and the recent Monte Carlo Tree Search algorithms, as two competing approaches for game tree evaluation, may be unified under the rollout paradigm.