An inverse optimization approach to decision-focused learning

Decision-focused learning is an emerging paradigm specifically aimed at improving the data-driven learning of input parameters to optimization models. The main idea is to learn predictive models that result in the best decisions rather than focusing on minimizing the parameter estimation error. Virtually all existing works on decision-focused learning only consider the case where the unknown model parameters merely affect the objective function. In this work, extend the framework to also consider unknown parameters in the constraints, where feasibility becomes a major concern. We address the problem by leveraging recently developed methods in data-driven inverse optimization, specifically applying a penalty-based block coordinate descent algorithm to solve the resulting large-scale bilevel optimization problem. The results from our computational case study demonstrate the effectiveness of the proposed approach and highlight its benefits compared with the conventional predict-then-optimize approach, which treats the prediction and optimization steps separately.