aiqbench analysis
This research advances data-driven inverse optimization for mixed-integer linear programs by jointly learning unknown constraints and objective functions, addressing a significant gap in existing methods that typically assume known constraints. The authors provide finite-sample theoretical guarantees using statistical learning tools for pseudo-metric spaces while validating the approach on complex scheduling instances with up to 100 decision variables. This work strengthens the mathematical foundations required for building accurate models in critical domains like power systems and industrial scheduling.
Inverse Mixed-Integer Programming: Learning Constraints then Objective Functions
arXiv:2510.04455v3 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 for MILPs 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.
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 for MILPs 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.
Optimization and Control (math.OC); Artificial Intelligence (cs.AI); Machine Learning (cs.LG); Statistics Theory (math.ST); Machine Learning (stat.ML)
arXiv:2510.04455 [math.OC]
(or arXiv:2510.04455v3 [math.OC] for this version)
Full text under the publisher's open licence · 223 words
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