# Scalable Kernel Inverse Optimization

arXiv: https://arxiv.org/abs/2410.23952 · HTML: https://mlsanity.com/paper/2410.23952/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 40 references that are in the map.
- First posted on arXiv 31 Oct 2024.

## Builds on (most cited first, 16 of 16)

- [Conservative Q-Learning for Offline Reinforcement Learning](https://mlsanity.com/paper/2006.04779/) (2020)
- [D4RL: Datasets for Deep Data-Driven Reinforcement Learning](https://mlsanity.com/paper/2004.07219/) (2020)
- [A Minimalist Approach to Offline Reinforcement Learning](https://mlsanity.com/paper/2106.06860/) (2021)
- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [Data-driven Distributionally Robust Optimization Using the Wasserstein Metric: Performance Guarantees and Tractable Reformulations](https://mlsanity.com/paper/1505.05116/) (2015)
- [Regularization via Mass Transportation](https://mlsanity.com/paper/1710.10016/) (2017)
- [Inverse Optimization: Theory and Applications](https://mlsanity.com/paper/2109.03920/) (2021)
- [Inverse Optimization with Noisy Data](https://mlsanity.com/paper/1507.03266/) (2015)
- [Data-Driven Estimation in Equilibrium Using Inverse Optimization](https://mlsanity.com/paper/1308.3397/) (2013)
- [A Primer on Coordinate Descent Algorithms](https://mlsanity.com/paper/1610.00040/) (2016)
- [Learning in Inverse Optimization: Incenter Cost, Augmented Suboptimality Loss, and Algorithms](https://mlsanity.com/paper/2305.07730/) (2023)
- [Inverse Optimization of Convex Risk Functions](https://mlsanity.com/paper/1607.07099/) (2016)
- [A Data-driven Bidding Model for a Cluster of Price-responsive Consumers of Electricity](https://mlsanity.com/paper/1506.06587/) (2015)
- [Quantile Inverse Optimization: Improving Stability in Inverse Linear Programming](https://mlsanity.com/paper/1908.02376/) (2019)
- [Forecasting the Price-Response of a Pool of Buildings via Homothetic Inverse Optimization](https://mlsanity.com/paper/2004.09819/) (2020)
- [Inverse Optimization for Routing Problems](https://mlsanity.com/paper/2307.07357/) (2023)

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

- [Online Inverse Linear Optimization: Efficient Logarithmic-Regret Algorithm, Robustness to Suboptimality, and Lower Bound](https://mlsanity.com/paper/2501.14349/) (2025)
- [Simple Projection-Free Algorithm for Contextual Recommendation with Logarithmic Regret and Robustness](https://mlsanity.com/paper/2603.20826/) (2026)
- [Offline Reinforcement Learning via Inverse Optimization](https://mlsanity.com/paper/2502.20030/) (2025)

## Abstract (arXiv)

Inverse Optimization (IO) is a framework for learning the unknown objective function of an expert decision-maker from a past dataset. In this paper, we extend the hypothesis class of IO objective functions to a reproducing kernel Hilbert space (RKHS), thereby enhancing feature representation to an infinite-dimensional space. We demonstrate that a variant of the representer theorem holds for a specific training loss, allowing the reformulation of the problem as a finite-dimensional convex optimization program. To address scalability issues commonly associated with kernel methods, we propose the Sequential Selection Optimization (SSO) algorithm to efficiently train the proposed Kernel Inverse Optimization (KIO) model. Finally, we validate the generalization capabilities of the proposed KIO model and the effectiveness of the SSO algorithm through learning-from-demonstration tasks on the MuJoCo benchmark.