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

arXiv: https://arxiv.org/abs/2210.15393 · HTML: https://mlsanity.com/paper/2210.15393/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 75 references that are in the map.
- First posted on arXiv 27 Oct 2022.

## Builds on (most cited first, 18 of 18)

- [The Loss Surfaces of Multilayer Networks](https://mlsanity.com/paper/1412.0233/) (2014)
- [Coordinate Descent Algorithms](https://mlsanity.com/paper/1502.04759/) (2015)
- [Non-convex Optimization for Machine Learning](https://mlsanity.com/paper/1712.07897/) (2017)
- [JuMP: A Modeling Language for Mathematical Optimization](https://mlsanity.com/paper/1508.01982/) (2015)
- [Inverse Optimization with Noisy Data](https://mlsanity.com/paper/1507.03266/) (2015)
- [Data-driven Inverse Optimization with Imperfect Information](https://mlsanity.com/paper/1512.05489/) (2015)
- [Data-Driven Estimation in Equilibrium Using Inverse Optimization](https://mlsanity.com/paper/1308.3397/) (2013)
- [Recent Theoretical Advances in Non-Convex Optimization](https://mlsanity.com/paper/2012.06188/) (2020)
- [Inverse Optimization: Closed-form Solutions, Geometry and Goodness of fit](https://mlsanity.com/paper/1511.04650/) (2015)
- [Inexact Block Coordinate Descent Algorithms for Nonsmooth Nonconvex Optimization](https://mlsanity.com/paper/1905.04211/) (2019)
- [Inverse optimization for the recovery of constraint parameters](https://mlsanity.com/paper/1811.00726/) (2018)
- [An Inverse Optimization Approach to Measuring Clinical Pathway Concordance](https://mlsanity.com/paper/1906.02636/) (2019)
- [A Data-driven Bidding Model for a Cluster of Price-responsive Consumers of Electricity](https://mlsanity.com/paper/1506.06587/) (2015)
- [Disciplined Multi-Convex Programming](https://mlsanity.com/paper/1609.03285/) (2016)
- [Quantile Inverse Optimization: Improving Stability in Inverse Linear Programming](https://mlsanity.com/paper/1908.02376/) (2019)
- [Decomposition and Adaptive Sampling for Data-Driven Inverse Linear Optimization](https://mlsanity.com/paper/2009.07961/) (2020)
- [Inferring Linear Feasible Regions using Inverse Optimization](https://mlsanity.com/paper/2001.00143/) (2020)
- [Comparing Inverse Optimization and Machine Learning Methods for Imputing a Convex Objective Function](https://mlsanity.com/paper/2102.10742/) (2021)

## Built on by (most cited first, 3 of 3)

- [Data-driven decision-focused surrogate modeling](https://mlsanity.com/paper/2308.12161/) (2023)
- [BO4IO: A Bayesian optimization approach to inverse optimization with uncertainty quantification](https://mlsanity.com/paper/2405.17875/) (2024)
- [Uncovering expert objectives in production planning via inverse optimization: An industrial case study](https://mlsanity.com/paper/2608.07398/) (2026)

## Abstract (arXiv)

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.