Tackling Morpion Solitaire with AlphaZero-like Ranked Reward Reinforcement Learning

Abstract

Morpion Solitaire is a popular single player game, performed with paper and pencil. Due to its large state space (on the order of the game of Go) traditional search algorithms, such as MCTS, have not been able to find good solutions. A later algorithm, Nested Rollout Policy Adaptation, was able to find a new record of 82 steps, albeit with large computational resources. After achieving this record, to the best of our knowledge, there has been no further progress reported, for about a decade.In this paper we take the recent impressive performance of deep self-learning reinforcement learning approaches from AlphaGo/AlphaZero as inspiration to design a searcher for Morpion Solitaire. A challenge of Morpion Solitaire is that the state space is sparse, there are few win/loss signals. Instead, we use an approach known as ranked reward to create a reinforcement learning self-play framework for Morpion Solitaire. This enables us to find medium-quality solutions with reasonable computational effort. Our record is a 67 steps solution, which is very close to the human best (68) without any other adaptation to the problem than using ranked reward. We list many further avenues for potential improvement.

Split Moves for Monte-Carlo Tree Search

“…More detailed results show that using semisplit in simulations gives a large efficiency boost and generally is not harmful in terms of their quality. This may be useful also apart from game playing, as simulations are applied to many single-player problems (Wang et al 2020). On the other hand, using semisplit in the MCTS tree gives some benefits in the quality of iterations, yet it is riskier, as sometimes it is consistently harmful (e.g., The Mill Game).…”

Adaptive Warm-Start MCTS in AlphaZero-Like Deep Reinforcement Learning

“…We set parameters values according to Table 1. The parameter choices are based on [Wang et al, 2020a].…”

“…There are many interesting works on self-play in reinforcement learning [Tesauro, 1995;Runarsson and Lucas, 2005;Plaat, 2020]. Temporal difference learning for acquiring position evaluation in small board Go with co-evolution has been compared to self-play [Runarsson and Lucas, 2005].…”