Addressing Over-fitting in Passive Constraint Acquisition through Active Learning

Vasileios Balafas, Dimos Tsouros, Nikolaos Ploskas, Kostas Stergiou

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Tracks: Special Session 2: Enhancing Exact Combinatorial Optimization Solvers with Machine Learning

Keywords: Constraint Programming, Active Learning, Constraint Acquisition, Global Constraints, Over-fitting

Abstract:

Constraint Programming (CP) is a powerful approach to solving complex combinatorial problems. However, formulating combinatorial problems as CP models typically demands substantial expertise. Constraint acquisition (CA) seeks to assist in model building by deriving constraints from data.
In passive learning, the system relies on a pre-labeled set of examples (solutions or non-solutions) to infer constraints, whereas active learning engages a domain expert or software system through targeted queries that classify newly proposed assignments to the variables of the problem. Hybrid CA frameworks that combine both strategies have also emerged to leverage the strengths of both approaches.
However, when training data are scarce or noisy, passive methods may overfit the observed examples—appearing valid on the training set but failing to generalize to other, unseen solutions—and thereby introduce invalid constraints into the model.
To address this issue that has been overlooked, we propose a new query-driven refinement approach that systematically challenges suspicious acquired constraints, using “violating assignments” designed to refute them while preserving all other constraints.
Focusing on the AllDifferent constraint, we integrate this refinement into an existing hybrid CA system and experimentally demonstrate that our approach facilitates convergence to a correct final model.

Submission Number: 73