Classifier-based constraint acquisition

Modeling a combinatorial problem is a hard and error-prone task requiring significant expertise. Constraint acquisition methods attempt to automate this process by learning constraints from examples of solutions and (usually) non-solutions. Active methods query an oracle while passive methods do not. We propose a known but not widely-used application of machine learning to constraint acquisition: training a classifier to discriminate between solutions and non-solutions, then deriving a constraint model from the trained classifier. We discuss a wide range of possible new acquisition methods with useful properties inherited from classifiers. We also show the potential of this approach using a Naive Bayes classifier, obtaining a new passive acquisition algorithm that is considerably faster than existing methods, scalable to large constraint sets, and robust under errors.

Chain Length and CSPs Learnable with Few Queries

The goal of constraint acquisition is to learn exactly a constraint network given access to an oracle that answers truthfully certain types of queries. In this paper we focus on partial membership queries and initiate a systematic investigation of the learning complexity of constraint languages. First, we use the notion of chain length to show that a wide class of languages can be learned with as few as O(n log(n)) queries. Then, we combine this result with generic lower bounds to derive a dichotomy in the learning complexity of binary languages. Finally, we identify a class of ternary languages that eludes our framework and hints at new research directions.