Pushing Data into CP Models Using Graphical Model Learning and Solving

Céline Brouard, Simon de Givry, Thomas Schiex

Abstract: Integrating machine learning with automated reasoning is one of the major goals of modern AI systems. In this paper, we propose a non-fully-differentiable architecture that is able to extract preferences from data and push it into (weighted) Constraint Networks (aka Cost Function Networks or CFN) by learning cost functions. Our approach combines a (scalable) convex optimization approach with empirical hyper-parameter tuning to learn cost functions from a list of high-quality solutions. The proposed architecture has the ability to learn from noisy solutions and its output is just a CFN model. This model can be analyzed, empirically hardened, completed with side-constraints, and directly fed to a Weighted Constraint Satisfaction Problem solver. To explore the performances and range of applicability of this architecture, we compare it with two recent neural-net friendly learning systems designed to “learn to reason” on the Sudoku problem and also show how it can be used to learn and integrate preferences into an existing CP model, in the context of Configuration systems.