arXiv:2405.14273v5 Announce Type: replace-cross Abstract: A data-driven inverse optimization problem (DDIOP) seeks to estimate an objective function (i.e., weights) that is consistent with observed optimal-solution data, and is important in many applications, including those involving mixed integer linear programs (MILPs). In the DDIOP for MILPs, the prediction loss on features (PLF), defined as the discrepancy between observed and predicted feature values, becomes discontinuous with respect to the weights, which makes it difficult to apply gradient-based optimization. To address this issue, we focus on a Lipschitz continuous and convex suboptimality loss. By exploiting its convex and piecewise-linear structure and the interiority of the minimum set, we show that a broad class of gradient-based optimization methods, including projected subgradient descent (PSGD), reaches the minimum suboptimality loss value in a finite number of iterations, thereby exactly solving the DDIOP for MILPs. Furthermore, as a corollary, we show that PSGD attains the minimum PLF in finitely many iterations. We also derive an upper bound on the number of iterations required for PSGD to reach finite convergence, and confirm the finite-step behavior through numerical experiments.

arXiv:2510.04455v2 Announce Type: replace-cross Abstract: Data-driven inverse optimization for mixed-integer linear programs (MILPs), which seeks to learn an objective function and constraints consistent with observed decisions, is important for building accurate mathematical models in a variety of domains, including power systems and scheduling. However, to the best of our knowledge, existing data-driven inverse optimization methods primarily focus on learning objective functions under known constraints, and learning both objective functions and constraints from data remains largely unexplored. In this paper, we propose a two-stage approach for a class of inverse optimization problems in which the objective is a linear combination of given feature functions and the constraints are parameterized by unknown functions and thresholds. Our method first learns the constraints and then, conditioned on the learned constraints, estimates the objective-function weights. On the theoretical side, we provide finite-sample guarantees for solving the proposed inverse optimization problem. To this end, we develop statistical learning tools for pseudo-metric spaces under sub-Gaussian assumptions and use them to derive a learning-theoretic framework for inverse optimization with both unknown objectives and constraints. On the experimental side, we demonstrate that our method successfully solves inverse optimization problems on scheduling instances formulated as ILPs with up to 100 decision variables.