Efficient multiple constraint acquisition

Abstract

Constraint acquisition systems such as QuAcq and MultiAcq can assist non-expert users to model their problems as constraint networks by classifying (partial) examples as positive or negative. For each negative example, the former focuses on one constraint of the target network, while the latter can learn a maximum number of constraints. Two bottlenecks of the acquisition process where both these algorithms encounter problems are the large number of queries required to reach convergence, and the high cpu times needed to generate queries, especially near convergence.In this paper we propose algorithmic and heuristic methods to deal with both these issues. We first describe an algorithm, called MQuAcq, that blends the main idea of MultiAcq into QuAcq resulting in a method that learns as many constraints as MultiAcq does after a negative example, but with a lower complexity. A detailed theoretical analysis of the proposed algorithm is also presented. Then we turn our attention to query generation which is a significant but rather overlooked part of the acquisition process. We describe how query generation in a typical constraint acquisition system operates, and we propose heuristics for improving its efficiency. Experiments from various domains demonstrate that our resulting algorithm that integrates all the new techniques does not only generate considerably fewer queries than QuAcq and MultiAcq, but it is also by far faster than both of them, in average query generation time as well as in total run time, and also largely alleviates the premature convergence problem.

Learning constraints through partial queries

“…One of the drawbacks of active constraint acquisition in general, and QuAcq1 in particular, is that generating membership queries can be very time-consuming. Attempts to reduce the time needed to generate a query were presented by Addi et al [1] and by Tsouros and Stergiou [42].…”

“…Unfortunately, this bounded time comes at the risk of failing to learn the target network (called premature convergence). In [42], several heuristics are proposed to speed up query generation. In QuAcq2, query generation does not suffer from premature convergence and the time to generate a query can be controlled by the use of a predefined time cutoff.…”

What Are the Rules? Discovering Constraints from Data

“…Learning constraints for constraint programming is a widely studied problem. Active learning approaches (Bessiere et al 2013;Tsouros and Stergiou 2020;Belaid et al 2022) derive constraints by asking queries in the form of partial or complete solutions and non-solutions. Even for simple problems, these approaches may require thousands of queries, which limits their applicability if a human must label these queries.…”

“…Existing approaches do not satisfactorily solve this task. Active learning (Bessiere et al 2013;Tsouros and Stergiou 2020;Belaid et al 2022) needs thousands of queries even for simple problems, which is intractable if a human expert must label these queries. Passive learning approaches (Pawlak and Krawiec 2017;Kumar et al 2020;Prestwich et al 2021) need invalid examples, i.e., non-solutions, in their training set.…”

Parallel Constraint Acquisition

“…GenerateExample. We can speed up the example generation by using well-known variable heuristic selectors (e.g., minDom, domOverWdeg, impact,...), or by using a dedicated one like bdeg heuristic (Tsouros and Stergiou 2020). bdeg selects the variable involved in a maximum number of constraints present in B i \ L. Knowing that each session is reasoning on a particular B i and based on preliminary comparisons, bdeg heuristic provides a good diversification.…”