Completeness of Unbounded Best-First Minimax and Descent Minimax
This addresses a foundational open question in game search algorithms, with implications for knowledge-free reinforcement learning, though it appears incremental as it builds on prior completion techniques.
The paper tackled the problem of whether the completion technique ensures that Unbounded Best-First Minimax and Descent Minimax algorithms can always determine a winning strategy in two-player perfect information games, showing that generalized versions of these algorithms compute the best strategy and experimentally demonstrating improved winning performance.
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.