Learning MAX-SAT from Contextual Examples for Combinatorial Optimisation

TL;DR

This paper introduces a new approach to learn MAX-SAT models for combinatorial optimization from contextual positive and negative examples, enabling easier model design without extensive expertise.

Contribution

The paper presents a novel framework for learning MAX-SAT models from contextual examples, including theoretical analysis and two practical implementations.

Findings

High-quality MAX-SAT models can be learned from examples under certain conditions.

The stochastic local search method scales better and performs comparably or better than syntax-guided synthesis.

Experimental results confirm the learnability of models from synthetic and benchmark data.

Abstract

Combinatorial optimisation problems are ubiquitous in artificial intelligence. Designing the underlying models, however, requires substantial expertise, which is a limiting factor in practice. The models typically consist of hard and soft constraints, or combine hard constraints with an objective function. We introduce a novel setting for learning combinatorial optimisation problems from contextual examples. These positive and negative examples show - in a particular context - whether the solutions are good enough or not. We develop our framework using the MAX-SAT formalism as it is simple yet powerful setting having these features. We study the learnability of MAX-SAT models. Our theoretical results show that high-quality MAX-SAT models can be learned from contextual examples in the realisable and agnostic settings, as long as the data satisfies an intuitive "representativeness" condition. We also contribute two implementations based on our theoretical results: one leverages ideas from syntax-guided synthesis while the other makes use of stochastic local search techniques. The two implementations are evaluated by recovering synthetic and benchmark models from contextual examples. The experimental results support our theoretical analysis, showing that MAX-SAT models can be learned from contextual examples. Among the two implementations, the stochastic local search learner scales much better than the syntax-guided implementation while providing comparable or better models.