Learning to Optimize with Hidden Constraints

The topic of learning to solve optimization problems has received interest from both the operations research and machine learning communities where each considers contrasting approaches: conditional stochastic optimization frameworks solved using provably optimal structured models versus deep learning models that leverage large data sets to yield empirically effective decision estimators. In this work, we combine the best of both worlds to solve the problem of learning to generate decisions to instances of continuous optimization problems where the feasible set varies with contextual features. We propose a novel framework for training a generative model to estimate optimal decisions by combining interior point methods and adversarial learning which we further embed within an active learning algorithm. Decisions generated by our model satisfy in-sample and out-of-sample optimality guarantees. Finally, we investigate case studies in portfolio optimization and personalized treatment design, demonstrating that our approach yields significant advantages over predict-then-optimize and supervised deep learning techniques, respectively.