Orateur
Description
As industry seeks to make its processes more resilient, data driven optimization is gaining momentum in Operation Research. Resilience involves managing uncertainty when optimizing supply chains, while efficiency requires scalable combinatorial optimization algorithms, as most gains from operations research algorithms come from decreasing marginal costs. This underscores the need for scalable algorithms for combinatorial and stochastic optimization problems, whether they are dynamic, tactical, or strategic. Policies encoded as neural networks with a combinatorial optimization layer have demonstrated their efficiency in these settings when trained in a decision-focused manner. Until now, such policies have been trained using supervised learning, often based on Fenchel-Young losses, and considered as heuristics. We instead focus on risk minimization. By leveraging the connection between Fenchel-Young losses and Bregman divergences, we introduce a deep learning-compatible primal-dual algorithm and show that it converges to the optimum of the empirical risk minimization problem in some settings. This new approach has two advantages. First, numerical experiments show that it learns better policies. Second, we prove some generalization properties that provide upper bounds on the optimality gap, which hold in expectation.
