On some improvements to Unbounded Minimax

TL;DR

This paper experimentally evaluates four modifications to the Unbounded Best-First Minimax algorithm, demonstrating how specific enhancements can improve its efficiency in game tree exploration.

Contribution

The paper provides the first experimental comparison of four untested modifications to Unbounded Best-First Minimax, including transposition tables, backpropagation strategies, heuristic evaluations, and completion techniques.

Findings

Transposition tables improve efficiency by merging duplicate states.

Modified backpropagation strategy slightly enhances performance.

Using learned heuristics reduces performance when evaluations are inexpensive.

Abstract

This paper presents the first experimental evaluation of four previously untested modifications of Unbounded Best-First Minimax algorithm. This algorithm explores the game tree by iteratively expanding the most promising sequences of actions based on the current partial game tree. We first evaluate the use of transposition tables, which convert the game tree into a directed acyclic graph by merging duplicate states. Second, we compare the original algorithm by Korf & Chickering with the variant proposed by Cohen-Solal, which differs in its backpropagation strategy: instead of stopping when a stable value is encountered, it updates values up to the root. This change slightly improves performance when value ties or transposition tables are involved. Third, we assess replacing the exact terminal evaluation function with the learned heuristic function. While beneficial when exact evaluations are costly, this modification reduces performance in inexpensive settings. Finally, we examine the impact of the completion technique that prioritizes resolved winning states and avoids resolved losing states. This technique also improves performance. Overall, our findings highlight how targeted modifications can enhance the efficiency of Unbounded Best-First Minimax.