Completeness of Unbounded Best-First Minimax and Descent Minimax
Summary: arXiv:2603.24572v1 Announce Type: new
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.
Introduction
Search algorithms play a crucial role in the domain of two-player perfect information games. These algorithms are designed to analyze possible game states and derive strategies that maximize a player’s chances of winning. However, the effectiveness of these algorithms can vary significantly. The Unbounded Best-First Minimax and Descent Minimax algorithms have shown potential but have limitations regarding their ability to consistently identify winning strategies.
Challenges in Existing Algorithms
The primary limitation of the Unbounded Best-First Minimax and Descent Minimax algorithms lies in their incompleteness. Even when provided with infinite search time, these algorithms do not guarantee the identification of a winning strategy. This poses a significant barrier for their application in real-world scenarios where optimal strategy determination is essential.
Improving Algorithmic Performance
To address these limitations, researchers have introduced a completion technique aimed at enhancing the performance of the aforementioned algorithms. Despite these advancements, the question of whether the completion technique sufficiently equips these algorithms to consistently determine a winning strategy remained an open question until now.
Research Findings
In our latest research, we have generalized the Unbounded Best-First Minimax and Descent Minimax algorithms, focusing on their variants that incorporate the completion technique. Our findings demonstrate that any algorithm within this generalized class is capable of computing the best strategy for two-player perfect information games.
Experiments and Performance Evaluation
To validate our theoretical findings, we conducted extensive experimental evaluations. The results indicate a marked improvement in winning performance when utilizing the completion technique. This enhancement not only confirms the efficacy of the generalization but also provides a robust framework for future research in the field of game strategy optimization.
Conclusion
The completion technique has proven to be a pivotal advancement in the functionality of the Unbounded Best-First Minimax and Descent Minimax algorithms. By generalizing these algorithms, we have established their capability to consistently derive the best strategies in two-player perfect information games. This work opens new avenues for research and application in knowledge-free reinforcement learning, contributing to the development of more effective game-playing strategies.
Future Directions
As we move forward, further research is needed to explore additional enhancements and applications of these algorithms in various domains. The findings from our study are expected to inspire further innovations in the realm of artificial intelligence and strategic decision-making.