Improving SAT Solver Heuristics with Graph Networks and Reinforcement Learning

Vitaly Kurin, Saad Godil, Shimon Whiteson, Bryan Catanzaro

Keywords: SAT, reinforcement learning, graph neural networks, heuristics, DQN, boolean satisfiability

TL;DR: We use reinforcement learning with graph neural networks to augment a branching heuristic of a SAT solver achieving 2-3X reduction in the number of iterations and generalizing to problems up to 5X larger than the training set.

Abstract: We present GQSAT, a branching heuristic in a Boolean SAT solver trained with value-based reinforcement learning (RL) using Graph Neural Networks for function approximation. Solvers using GQSAT are complete SAT solvers that either provide a satisfying assignment or a proof of unsatisfiability, which is required for many SAT applications. The branching heuristic commonly used in SAT solvers today suffers from bad decisions during their warm-up period, whereas GQSAT has been trained to examine the structure of the particular problem instance to make better decisions at the beginning of the search. Training GQSAT is data efficient and does not require elaborate dataset preparation or feature engineering to train. We train GQSAT on small SAT problems using RL interfacing with an existing SAT solver. We show that GQSAT is able to reduce the number of iterations required to solve SAT problems by 2-3X, and it generalizes to unsatisfiable SAT instances, as well as to problems with 5X more variables than it was trained on. We also show that, to a lesser extent, it generalizes to SAT problems from different domains by evaluating it on graph coloring. Our experiments show that augmenting SAT solvers with agents trained with RL and graph neural networks can improve performance on the SAT search problem.

Community Implementations: [ 1 code implementation](https://www.catalyzex.com/paper/arxiv:1909.11830/code)