Teaching the old dog new tricks: Supervised learning with constraints

Methods for taking into account external knowledge in Machine Learning models have the potential to address outstanding issues in data-driven AI methods, such as improving safety and fairness, and can simplify training in the presence of scarce data. We propose a simple, but effective, method for injecting constraints at training time in supervised learning, based on decomposition and bi-level optimization: a master step is in charge of enforcing the constraints, while a learner step takes care of training the model. The process leads to approximate constraint satisfaction. The method is applicable to any ML approach for which the concept of label (or target) is well defined (most regression and classification scenarios), and allows to reuse existing training algorithms with no modifications. We require no assumption on the constraints, although their properties affect the shape and complexity of the master problem. Convergence guarantees are hard to provide, but we found that the approach performs well on ML tasks with fairness constraints and on classical datasets with synthetic constraints