Empirical Model Learning for Constrained Black Box Optimization

Black box optimization is a field of the global optimization which consists in a family of methods intended to minimize or maximize an objective function that doesn’t allow the exploitation of gradients, linearity or convexity information. Beside that the objective is often a problem that requires a significant amount of time/resources to query a point and thus the goal is to go as close as possible to the optimum with the less number of iterations possible. The Emprical Model Learning is a methodology for merging Machine Learning and optimization techniques like Constraint Programming and Mixed Integer Linear Programming by extracting decision models from the data. This work aims to close the gap between Empirical Model Learning optimization and Black Box optimization methods (which have a strong literature) via active learning. At each iteration of the optimization loop a ML model is fitted on the data points and it is embedded in a prescriptive model using the EML. The encoded model is then enriched with domain specific constraints and is optimized selecting the next point to query and add to the collection of samples.