A Novel Approach to Solving Goal-Achieving Problems for Board Games

TL;DR

This paper introduces RZ-Based Search (RZS), a novel null-move-free algorithm for goal-achieving problems in Go, enhanced by a new training method called Faster to Life (FTL), significantly improving problem-solving success rates.

Contribution

The paper presents RZS, a new RZ-based search algorithm that eliminates null move heuristics, and FTL, a training method to accelerate AlphaZero's goal achievement in Go.

Findings

Solved 68 out of 106 L&D problems, outperforming previous methods.

RZS can be integrated into AlphaZero for enhanced goal-solving.

FTL accelerates AlphaZero's ability to win quickly in goal-oriented tasks.

Abstract

Goal-achieving problems are puzzles that set up a specific situation with a clear objective. An example that is well-studied is the category of life-and-death (L&D) problems for Go, which helps players hone their skill of identifying region safety. Many previous methods like lambda search try null moves first, then derive so-called relevance zones (RZs), outside of which the opponent does not need to search. This paper first proposes a novel RZ-based approach, called the RZ-Based Search (RZS), to solving L&D problems for Go. RZS tries moves before determining whether they are null moves post-hoc. This means we do not need to rely on null move heuristics, resulting in a more elegant algorithm, so that it can also be seamlessly incorporated into AlphaZero's super-human level play in our solver. To repurpose AlphaZero for solving, we also propose a new training method called Faster to Life (FTL), which modifies AlphaZero to entice it to win more quickly. We use RZS and FTL to solve L&D problems on Go, namely solving 68 among 106 problems from a professional L&D book while a previous program solves 11 only. Finally, we discuss that the approach is generic in the sense that RZS is applicable to solving many other goal-achieving problems for board games.