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[2405.14273] Exact Solution to Data-Driven Inverse Optimization of MILPs in Finite Time via Gradient-Based Methods
Summary
This article presents an exact solution to data-driven inverse optimization of mixed integer linear programs (MILPs) using gradient-based methods, demonstrating finite convergence through numerical experiments.
Why It Matters
The findings are significant for optimizing MILPs, which are widely used in various fields, including logistics and finance. By providing a method that guarantees finite convergence, this research enhances the efficiency and reliability of optimization processes, making it valuable for practitioners and researchers in machine learning and operations research.
Key Takeaways
- Introduces a data-driven inverse optimization problem (DDIOP) for MILPs.
- Demonstrates that gradient-based methods can achieve finite convergence.
- Establishes an upper bound on the number of iterations required for convergence.
- Provides numerical experiments confirming the theoretical results.
- Highlights the importance of Lipschitz continuous and convex suboptimality loss.
Computer Science > Machine Learning arXiv:2405.14273 (cs) [Submitted on 23 May 2024 (v1), last revised 16 Feb 2026 (this version, v5)] Title:Exact Solution to Data-Driven Inverse Optimization of MILPs in Finite Time via Gradient-Based Methods Authors:Akira Kitaoka View a PDF of the paper titled Exact Solution to Data-Driven Inverse Optimization of MILPs in Finite Time via Gradient-Based Methods, by Akira Kitaoka View PDF HTML (experimental) 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. W...
