Solving QSAT problems with neural MCTS
This work addresses QSAT solving, a hard computational problem, by applying neural MCTS, but it is incremental as it builds on existing AlphaZero methods and is limited to small-scale instances.
The authors tackled solving Quantified Boolean Formula Satisfaction (QSAT) problems, which are PSPACE-complete, by adapting neural Monte Carlo Tree Search (MCTS) from AlphaZero with graph neural networks, and achieved correct solutions for limited-size problems through self-play training.
Recent achievements from 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 try to leverage the computational power of neural Monte Carlo Tree Search (neural MCTS), the core algorithm from AlphaZero, to solve Quantified Boolean Formula Satisfaction (QSAT) problems, which are PSPACE complete. Knowing that every QSAT problem is equivalent to a QSAT game, the game outcome can be used to derive the solutions of the original QSAT problems. 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.