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 a 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.

组合优化问题在人工智能中无处不在。然而，设计基础模型需要大量的专业知识，这在实践中是一个限制因素。这些模型通常由硬约束和软约束组成，或者将硬约束与目标函数结合起来。我们引入了一种从上下文学习组合优化问题的新设置例子。这些正面和负面的例子表明——在特定的背景下——解决方案是否足够好。我们使用 MAX-SAT 形式开发我们的框架，因为它是具有这些功能的简单而强大的设置。我们研究了 MAX-SAT 模型的可学习性。我们的理论结果表明，只要数据满足直观的“代表性”条件，就可以从可实现和不可知设置中的上下文示例中学习高质量的 MAX-SAT 模型。我们还根据我们的理论结果贡献了两种实现：一种利用了语法引导合成的思想，另一种利用了随机局部搜索技术。通过从上下文示例中恢复合成模型和基准模型来评估这两种实现。实验结果支持我们的理论分析，表明可以从上下文示例中学习 MAX-SAT 模型。在这两种实现中，随机局部搜索学习器的扩展性比语法引导的实现好得多，同时提供了可比或更好的模型。