Learning to resolve inconsistencies in qualitative constraint networks

Abstract

In this paper, we present a reinforcement learning approach for resolving inconsistencies in qualitative constraint networks ($\mathrm{QCN}$s). $\mathrm{QCN}$s are typically used in constraint programming to represent and reason about intuitive spatial or temporal relations like x {is inside of $\vee$ overlaps} y. Naturally, $\mathrm{QCN}$s are not immune to uncertainty, noise, or imperfect data that may be present in information, and thus, more often than not, they are hampered by inconsistencies. We propose a multi-armed bandit approach that defines a well-suited ordering of constraints for finding a maximal satisfiable subset of them. Specifically, our learning approach interacts with a solver, and after each trial a reward is returned to measure the performance of the selected action (constraint addition). The reward function is based on the reduction of the solution space of a consistent reconstruction of the input $\mathrm{QCN}$. Experimental results with different bandit policies and various rewards that are obtained by our algorithm suggest that we can do better than the state of the art in terms of both effectiveness, viz., lower number of repairs obtained for an inconsistent $\mathrm{QCN}$, and efficiency, viz., faster runtime.