Decision-making problems are commonly formulated as optimization problems, which are then solved to make optimal decisions. In this work, we consider the inverse problem where we use prior decision data to uncover the underlying decision-making process in the form of a mathematical optimization model. This statistical learning problem is referred to as data-driven inverse optimization. We focus on problems where the underlying decision-making process is modeled as a convex optimization problem whose parameters are unknown. We formulate the inverse optimization problem as a bilevel program and propose an efficient block coordinate descent-based algorithm to solve large problem instances. Numerical experiments on synthetic datasets demonstrate the computational advantage of our method compared to standard commercial solvers. Moreover, the real-world utility of the proposed approach is highlighted through two realistic case studies in which we consider estimating risk preferences and learning local constraint parameters of agents in a multiplayer Nash bargaining game.
Bibliographical noteFunding Information:
The authors gratefully acknowledge the financial support from the National Science Foundation, USA under Grant #2044077 as well as the Minnesota Supercomputing Institute (MSI) at the University of Minnesota for providing resources that contributed to the research results reported in this paper. R.G. acknowledges financial support from a departmental fellowship sponsored by 3M and a Doctoral Dissertation Fellowship from the University of Minnesota, USA .
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- Bilevel optimization
- Block coordinate descent
- Data-driven inverse optimization
- Statistical learning