# Inverse Optimization: Theory and Applications

arXiv: https://arxiv.org/abs/2109.03920 · HTML: https://mlsanity.com/paper/2109.03920/

## Key facts

- Cited by 48 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Sep 2021.

## Built on by (most cited first, 30 of 48)

- [A Survey of Contextual Optimization Methods for Decision Making under Uncertainty](https://mlsanity.com/paper/2306.10374/) (2023)
- [Decision Theoretic Foundations for Conformal Prediction: Optimal Uncertainty Quantification for Risk-Averse Agents](https://mlsanity.com/paper/2502.02561/) (2025)
- [Network Diffuser for Placing-Scheduling Service Function Chains with Inverse Demonstration](https://mlsanity.com/paper/2501.05673/) (2025)
- [Learning in Inverse Optimization: Incenter Cost, Augmented Suboptimality Loss, and Algorithms](https://mlsanity.com/paper/2305.07730/) (2023)
- [Online Inverse Linear Optimization: Efficient Logarithmic-Regret Algorithm, Robustness to Suboptimality, and Lower Bound](https://mlsanity.com/paper/2501.14349/) (2025)
- [Learning of Population Dynamics: Inverse Optimization Meets JKO Scheme](https://mlsanity.com/paper/2506.01502/) (2025)
- [Revisiting Online Learning Approach to Inverse Linear Optimization: A Fenchel-Young Loss Perspective and Gap-Dependent Regret Analysis](https://mlsanity.com/paper/2501.13648/) (2025)
- [Finite and Corruption-Robust Regret Bounds in Online Inverse Linear Optimization under M-Convex Action Sets](https://mlsanity.com/paper/2602.01682/) (2026)
- [Simple Projection-Free Algorithm for Contextual Recommendation with Logarithmic Regret and Robustness](https://mlsanity.com/paper/2603.20826/) (2026)
- [Tight Generalization Bounds for Noiseless Inverse Optimization](https://mlsanity.com/paper/2605.08866/) (2026)
- [Inverse Optimization for Routing Problems](https://mlsanity.com/paper/2307.07357/) (2023)
- [ReGuidance: A Simple Diffusion Wrapper for Boosting Sample Quality on Hard Inverse Problems](https://mlsanity.com/paper/2506.10955/) (2025)
- [Universal Inverse Distillation for Matching Models with Real-Data Supervision (No GANs)](https://mlsanity.com/paper/2509.22459/) (2025)
- [Data-driven decision-focused surrogate modeling](https://mlsanity.com/paper/2308.12161/) (2023)
- [Exact Solution to Data-Driven Inverse Optimization of MILPs in Finite Time via Gradient-Based Methods](https://mlsanity.com/paper/2405.14273/) (2024)
- [Offline Hierarchical Reinforcement Learning via Inverse Optimization](https://mlsanity.com/paper/2410.07933/) (2024)
- [Optimal Decision-Making Based on Prediction Sets](https://mlsanity.com/paper/2602.00989/) (2026)
- [From Inverse Optimization to Feasibility to ERM](https://mlsanity.com/paper/2402.17890/) (2024)
- [Counterfactual Explanations for Linear Optimization](https://mlsanity.com/paper/2405.15431/) (2024)
- [BO4IO: A Bayesian optimization approach to inverse optimization with uncertainty quantification](https://mlsanity.com/paper/2405.17875/) (2024)
- [Scalable Kernel Inverse Optimization](https://mlsanity.com/paper/2410.23952/) (2024)
- [Efficient Inverse Multiagent Learning](https://mlsanity.com/paper/2502.14160/) (2025)
- [Conformalized Decision Risk Assessment](https://mlsanity.com/paper/2505.13243/) (2025)
- [Efficient Online Inverse Optimization with O(d) Regret](https://mlsanity.com/paper/2609.13440/) (2026)
- [Block Sparse Bayesian Learning: A Diversified Scheme](https://mlsanity.com/paper/2402.04646/) (2024)
- [Inverse Mixed-Integer Programming: Learning Constraints then Objective Functions](https://mlsanity.com/paper/2510.04455/) (2025)
- [Conformal Risk-Averse Decision Making with Action Conditional Guarantee](https://mlsanity.com/paper/2606.05551/) (2026)
- [Bilevel Optimization for Neural Architecture Search](https://mlsanity.com/paper/2606.29582/) (2026)
- [Explicit Iteration Complexity of Exact Data-Driven Inverse Optimization for Integer Linear Programs](https://mlsanity.com/paper/2607.22263/) (2026)
- [Tight Regret Bound for Online Inverse Linear Optimization via Multiscale Matrix Weights](https://mlsanity.com/paper/2609.26978/) (2026)

## Abstract (arXiv)

Inverse optimization describes a process that is the "reverse" of traditional mathematical optimization. Unlike traditional optimization, which seeks to compute optimal decisions given an objective and constraints, inverse optimization takes decisions as input and determines an objective and/or constraints that render these decisions approximately or exactly optimal. In recent years, there has been an explosion of interest in the mathematics and applications of inverse optimization. This paper provides a comprehensive review of both the methodological and application-oriented literature in inverse optimization.