Streamlining Variational Inference for Constraint Satisfaction Problems
This work addresses a specific issue in solving constraint satisfaction problems, offering an incremental improvement for researchers and practitioners in computational logic and AI.
The paper tackled the problem of approximate and self-contradictory marginal estimates in constraint satisfaction problems by introducing a branching strategy based on streamlining constraints, resulting in a 16.3% average reduction in the gap between empirical performance and theoretical limits for random k-SAT instances.
Several algorithms for solving constraint satisfaction problems are based on survey propagation, a variational inference scheme used to obtain approximate marginal probability estimates for variable assignments. These marginals correspond to how frequently each variable is set to true among satisfying assignments, and are used to inform branching decisions during search; however, marginal estimates obtained via survey propagation are approximate and can be self-contradictory. We introduce a more general branching strategy based on streamlining constraints, which sidestep hard assignments to variables. We show that streamlined solvers consistently outperform decimation-based solvers on random k-SAT instances for several problem sizes, shrinking the gap between empirical performance and theoretical limits of satisfiability by 16.3% on average for k=3,4,5,6.