Constraint Programming (CP) has been successfully used to model and solve complex combinatorial problems. However, modeling is often not trivial and requires expertise, which is a bottleneck to wider adoption. In Constraint Acquisition (CA), the goal is to assist the user by automatically learning the model. In (inter)active CA, this is done by interactively posting queries to the user, e.g., asking whether a partial solution satisfies their (unspecified) constraints or not. While interac tive CA methods learn the constraints, the learning is related to symbolic concept learning, as the goal is to learn an exact representation. However, a large number of queries is still required to learn the model, which is a major limitation. In this paper, we aim to alleviate this limitation by tightening the connection of CA and Machine Learning (ML), by, for the first time in interactive CA, exploiting statistical ML methods. We propose to use probabilistic classification models to guide interactive CA to generate more promising queries. We discuss how to train classifiers to predict whether a candidate expression from the bias is a constraint of the problem or not, using both relation-based and scope-based features. We then show how the predictions can be used in all layers of interactive CA: the query generation, the scope finding, and the lowest-level constraint finding. We experimentally evaluate our proposed methods using different classifiers and show that our methods greatly outperform the state of the art, decreasing the number of queries needed to converge by up to 72%.

翻译：约束规划（Constraint Programming, CP）已成功用于建模和求解复杂组合问题。然而，建模过程通常并非易事且需要专业知识，这成为制约其更广泛应用的瓶颈。在约束获取（Constraint Acquisition, CA）中，目标是通过自动学习模型来辅助用户。在（交）互式CA中，这通过交互式地向用户发送查询来实现，例如询问某个部分解是否满足其（未指定的）约束。尽管交互式CA方法能够学习约束，但其学习过程类似于符号概念学习，目标是获取精确的表示。然而，学习模型仍需要大量的查询，这是一个主要局限。本文旨在通过首次在交互式CA中利用统计机器学习（Machine Learning, ML）方法，加强CA与ML的联系以缓解这一局限。我们提出使用概率分类模型来引导交互式CA生成更有前景的查询。我们探讨如何训练分类器，利用基于关系和基于作用域的特征，预测偏置中的候选表达式是否为问题的约束。随后，我们展示如何将预测应用于交互式CA的各个层级：查询生成、作用域发现及底层约束发现。通过使用不同分类器对所提方法进行实验评估，结果表明我们的方法显著优于现有技术，将收敛所需的查询数量最多减少72%。