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Efficient Learning of Decision-Making Models: A Penalty Block Coordinate Descent Algorithm for Data-Driven Inverse Optimization

Rishabh GuptaQi Zhang
Oct 2022
摘要
Decision-making problems are commonly formulated as optimization problems,which are then solved to make optimal decisions. In this work, we consider theinverse problem where we use prior decision data to uncover the underlyingdecision-making process in the form of a mathematical optimization model. Thisstatistical learning problem is referred to as data-driven inverseoptimization. We focus on problems where the underlying decision-making processis modeled as a convex optimization problem whose parameters are unknown. Weformulate the inverse optimization problem as a bilevel program and propose anefficient block coordinate descent-based algorithm to solve large probleminstances. Numerical experiments on synthetic datasets demonstrate thecomputational advantage of our method compared to standard commercial solvers.Moreover, the real-world utility of the proposed approach is highlightedthrough two realistic case studies in which we consider estimating riskpreferences and learning local constraint parameters of agents in a multiplayerNash bargaining game.
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