Towards Tackling QSAT Problems with Deep Learning and Monte Carlo Tree Search

Abstract

AbstractRecent achievements of AlphaZero using self-play has shown remarkable performance on several board games. It is plausible to think that self-play, starting from zero knowledge, can gradually approximate a winning strategy for certain two-player games after an amount of training. In this paper, we present a proof-of-concept to solve small instances of Quantified Boolean Formula Satisfaction (QSAT) problems by leveraging the computational power from neural Monte Carlo Tree Search (neural MCTS). QSAT is a PSPACE-complete problem with many practical applications. We propose a way to encode Quantified Boolean Formulas (QBFs) as graphs and apply a graph neural network (GNN) to embed the QBFs into the neural MCTS. After training, an off-the-shelf QSAT solver is used to evaluate the performance of the algorithm. Our result shows that, for problems within a limited size, the algorithm learns to solve the problem correctly merely from self-play. It is impressive that neural MCTS is succeeding on small QSAT problems but research is needed to better understand the algorithm and its parameters. KeywordsNeural MCTSGraph neural networkQSAT