# Interpreting Robust Optimization via Adversarial Influence Functions

arXiv: https://arxiv.org/abs/2010.01247 · HTML: https://mlsanity.com/paper/2010.01247/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Oct 2020.

## Built on by (most cited first, 8 of 8)

- [When and How Mixup Improves Calibration](https://mlsanity.com/paper/2102.06289/) (2021)
- [Adversarial Training Helps Transfer Learning via Better Representations](https://mlsanity.com/paper/2106.10189/) (2021)
- [FIFA: Making Fairness More Generalizable in Classifiers Trained on Imbalanced Data](https://mlsanity.com/paper/2206.02792/) (2022)
- [DeepAdversaries: Examining the Robustness of Deep Learning Models for Galaxy Morphology Classification](https://mlsanity.com/paper/2112.14299/) (2021)
- [Influence Functions for Sequence Tagging Models](https://mlsanity.com/paper/2210.14177/) (2022)
- [Reinforcement Learning with Stepwise Fairness Constraints](https://mlsanity.com/paper/2211.03994/) (2022)
- [Evaluating the Impact of Local Differential Privacy on Utility Loss via Influence Functions](https://mlsanity.com/paper/2309.08678/) (2023)
- [Safety-Efficacy Trade Off: Robustness against Data-Poisoning](https://mlsanity.com/paper/2602.00822/) (2026)

## Abstract (arXiv)

Robust optimization has been widely used in nowadays data science, especially in adversarial training. However, little research has been done to quantify how robust optimization changes the optimizers and the prediction losses comparing to standard training. In this paper, inspired by the influence function in robust statistics, we introduce the Adversarial Influence Function (AIF) as a tool to investigate the solution produced by robust optimization. The proposed AIF enjoys a closed-form and can be calculated efficiently. To illustrate the usage of AIF, we apply it to study model sensitivity -- a quantity defined to capture the change of prediction losses on the natural data after implementing robust optimization. We use AIF to analyze how model complexity and randomized smoothing affect the model sensitivity with respect to specific models. We further derive AIF for kernel regressions, with a particular application to neural tangent kernels, and experimentally demonstrate the effectiveness of the proposed AIF. Lastly, the theories of AIF will be extended to distributional robust optimization.