Learning in Inverse Optimization: Incenter Cost, Augmented Suboptimality Loss, and Algorithms

• 成果类型: Article
• 署名作者: Scroccaro, Pedro Zattoni; Atasoy, Bilge; Esfahani, Peyman Mohajerin
• 署名单位: Delft University of Technology; Delft University of Technology
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2023.0254
• 发表日期: 2025
• 关键词: variational-inequalities

摘要

In inverse optimization (IO), an expert agent solves an optimization problem parametric in an exogenous signal. From a learning perspective, the goal is to learn the expert's cost function given a data set of signals and corresponding optimal actions. Motivated by the geometry of the IO set of consistent cost vectors, we introduce the incenter concept, a new notion akin to the recently proposed circumcenter concept. Discussing the geometric and robustness interpretation of the incenter cost vector, we develop corresponding tractable convex reformulations that are in contrast with the circumcenter, which we show is equivalent to an intractable optimization program. We further propose a novel loss function called augmented suboptimality loss (ASL), a relaxation of the incenter concept for problems with inconsistent data. Exploiting the structure of the ASL, we propose a novel first-order algorithm, which we name stochastic approximate mirror descent. This algorithm combines stochastic and approximate subgradient evaluations, together with mirror descent update steps, which are provably efficient for the IO problems with discrete feasible sets with high cardinality. We implement the IO approaches developed in this paper as a Python package called InvOpt. Our numerical experiments are reproducible, and the underlying source code is available as examples in the InvOpt package.