# Generalized Inverse Optimization through Online Learning

arXiv: https://arxiv.org/abs/1810.01920 · HTML: https://mlsanity.com/paper/1810.01920/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Oct 2018.

## Built on by (most cited first, 12 of 12)

- [Contextual Inverse Optimization: Offline and Online Learning](https://mlsanity.com/paper/2106.14015/) (2021)
- [Online Inverse Linear Optimization: Efficient Logarithmic-Regret Algorithm, Robustness to Suboptimality, and Lower Bound](https://mlsanity.com/paper/2501.14349/) (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)
- [Robo-Advising: Enhancing Investment with Inverse Optimization and Deep Reinforcement Learning](https://mlsanity.com/paper/2105.09264/) (2021)
- [Repeated Principal-Agent Games with Unobserved Agent Rewards and Perfect-Knowledge Agents](https://mlsanity.com/paper/2304.07407/) (2023)
- [Estimating and Incentivizing Imperfect-Knowledge Agents with Hidden Rewards](https://mlsanity.com/paper/2308.06717/) (2023)
- [Using Inverse Optimization to Learn Cost Functions in Generalized Nash Games](https://mlsanity.com/paper/2102.12415/) (2021)
- [Towards Generalized Inverse Reinforcement Learning](https://mlsanity.com/paper/2402.07246/) (2024)
- [Machine Learning for Combinatorial Optimisation of Partially-Specified Problems: Regret Minimisation as a Unifying Lens](https://mlsanity.com/paper/2205.10157/) (2022)
- [Social-Inverse: Inverse Decision-making of Social Contagion Management with Task Migrations](https://mlsanity.com/paper/2209.10493/) (2022)
- [A Fenchel-Young Loss Approach to Data-Driven Inverse Optimization](https://mlsanity.com/paper/2502.16120/) (2025)
- [Mathematical Programming in Machine Learning and Artificial Intelligence: A Unified Taxonomy of Models and Applications](https://mlsanity.com/paper/2609.07254/) (2026)

## Abstract (arXiv)

Inverse optimization is a powerful paradigm for learning preferences and restrictions that explain the behavior of a decision maker, based on a set of external signal and the corresponding decision pairs. However, most inverse optimization algorithms are designed specifically in batch setting, where all the data is available in advance. As a consequence, there has been rare use of these methods in an online setting suitable for real-time applications. In this paper, we propose a general framework for inverse optimization through online learning. Specifically, we develop an online learning algorithm that uses an implicit update rule which can handle noisy data. Moreover, under additional regularity assumptions in terms of the data and the model, we prove that our algorithm converges at a rate of O(1/√T) and is statistically consistent. In our experiments, we show the online learning approach can learn the parameters with great accuracy and is very robust to noises, and achieves a dramatic improvement in computational efficacy over the batch learning approach.