UNSAT Solver Synthesis via Monte Carlo Forest Search
This work addresses the challenge of scaling reinforcement learning for SAT solving, offering a method to reduce computational costs in automated theorem proving and optimization, though it is incremental as it builds on existing MCTS and RL techniques.
The paper tackled the problem of learning efficient branching policies for Boolean satisfiability (SAT) solvers, specifically for unsatisfiable instances, by introducing Monte Carlo Forest Search (MCFS) and an instantiation called Knuth Synthesis, which matched or exceeded baseline performance on three SAT distributions with problems two orders of magnitude more challenging than prior RL studies.
We introduce Monte Carlo Forest Search (MCFS), a class of reinforcement learning (RL) algorithms for learning policies in {tree MDPs}, for which policy execution involves traversing an exponential-sized tree. Examples of such problems include proving unsatisfiability of a SAT formula; counting the number of solutions of a satisfiable SAT formula; and finding the optimal solution to a mixed-integer program. MCFS algorithms can be seen as extensions of Monte Carlo Tree Search (MCTS) to cases where, rather than finding a good path (solution) within a tree, the problem is to find a small tree within a forest of candidate trees. We instantiate and evaluate our ideas in an algorithm that we dub Knuth Synthesis, an MCFS algorithm that learns DPLL branching policies for solving the Boolean satisfiability (SAT) problem, with the objective of achieving good average-case performance on a given distribution of unsatisfiable problem instances. Knuth Synthesis is the first RL approach to avoid the prohibitive costs of policy evaluations in an exponentially-sized tree, leveraging two key ideas: first, we estimate tree size by randomly sampling paths and measuring their lengths, drawing on an unbiased approximation due to Knuth (1975); second, we query a strong solver at a user-defined depth rather than learning a policy across the whole tree, to focus our policy search on early decisions that offer the greatest potential for reducing tree size. We matched or exceeded the performance of a strong baseline on three well-known SAT distributions, facing problems that were two orders of magnitude more challenging than those addressed in previous RL studies.