Efficient Learning of Decision-Making Models: A Penalty Block Coordinate Descent Algorithm for Data-Driven Inverse Optimization
This work addresses the challenge of uncovering hidden optimization models from decision data, which is incremental as it builds on existing inverse optimization methods with a focus on efficiency and scalability.
The paper tackles the problem of learning decision-making models from data, known as data-driven inverse optimization, by proposing a block coordinate descent algorithm to efficiently solve large instances, demonstrating computational advantages over standard solvers in synthetic tests and applying it to real-world case studies like estimating risk preferences and learning parameters in Nash bargaining games.
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.