Completeness of Unbounded Best-First Minimax and Descent Minimax

TL;DR

This paper investigates the completeness of unbounded best-first minimax and descent minimax algorithms in two-player perfect information games, proving their ability to compute optimal strategies when enhanced with the completion technique.

Contribution

It generalizes these algorithms with the completion technique and proves they can always determine the best strategy, addressing an open question in game search algorithms.

Findings

Generalized algorithms compute the best strategy.

Completion technique improves winning performance.

Algorithms are proven to be complete with the enhancement.

Abstract

In this article, we focus on search algorithms for two-player perfect information games, whose objective is to determine the best possible strategy, and ideally a winning strategy. Unfortunately, some search algorithms for games in the literature are not able to always determine a winning strategy, even with an infinite search time. This is the case, for example, of the following algorithms: Unbounded Best-First Minimax and Descent Minimax, which are core algorithms in state-of-the-art knowledge-free reinforcement learning. They were then improved with the so-called completion technique. However, whether this technique sufficiently improves these algorithms to allow them to always determine a winning strategy remained an open question until now. To answer this question, we generalize the two algorithms (their versions using the completion technique), and we show that any algorithm of this class of algorithms computes the best strategy. Finally, we experimentally show that the completion technique improves winning performance.