# Towards Calibrated Losses for Adversarial Robust Reject Option Classification

arXiv: https://arxiv.org/abs/2410.10736 · HTML: https://mlsanity.com/paper/2410.10736/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 27 references that are in the map.
- First posted on arXiv 14 Oct 2024.

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

- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Towards Evaluating the Robustness of Neural Networks](https://mlsanity.com/paper/1608.04644/) (2016)
- [Certified Adversarial Robustness via Randomized Smoothing](https://mlsanity.com/paper/1902.02918/) (2019)
- [Provable defenses against adversarial examples via the convex outer adversarial polytope](https://mlsanity.com/paper/1711.00851/) (2017)
- [Certified Defenses against Adversarial Examples](https://mlsanity.com/paper/1801.09344/) (2018)
- [Deep k-Nearest Neighbors: Towards Confident, Interpretable and Robust Deep Learning](https://mlsanity.com/paper/1803.04765/) (2018)
- [Rethinking Lipschitz Neural Networks and Certified Robustness: A Boolean Function Perspective](https://mlsanity.com/paper/2210.01787/) (2022)
- [ML-LOO: Detecting Adversarial Examples with Feature Attribution](https://mlsanity.com/paper/1906.03499/) (2019)
- [Calibration and Consistency of Adversarial Surrogate Losses](https://mlsanity.com/paper/2104.09658/) (2021)
- [On the Calibration of Multiclass Classification with Rejection](https://mlsanity.com/paper/1901.10655/) (2019)
- [Calibrated Surrogate Losses for Adversarially Robust Classification](https://mlsanity.com/paper/2005.13748/) (2020)
- [A Finer Calibration Analysis for Adversarial Robustness](https://mlsanity.com/paper/2105.01550/) (2021)
- [Towards Consistency in Adversarial Classification](https://mlsanity.com/paper/2205.10022/) (2022)
- [Online Active Learning of Reject Option Classifiers](https://mlsanity.com/paper/1906.06166/) (2019)
- [ATRO: Adversarial Training with a Rejection Option](https://mlsanity.com/paper/2010.12905/) (2020)
- [Stratified Adversarial Robustness with Rejection](https://mlsanity.com/paper/2305.01139/) (2023)

## Abstract (arXiv)

Robustness towards adversarial attacks is a vital property for classifiers in several applications such as autonomous driving, medical diagnosis, etc. Also, in such scenarios, where the cost of misclassification is very high, knowing when to abstain from prediction becomes crucial. A natural question is which surrogates can be used to ensure learning in scenarios where the input points are adversarially perturbed and the classifier can abstain from prediction? This paper aims to characterize and design surrogates calibrated in "Adversarial Robust Reject Option" setting. First, we propose an adversarial robust reject option loss ℓdγ and analyze it for the hypothesis set of linear classifiers (H_textrmlin). Next, we provide a complete characterization result for any surrogate to be (ℓdγ,H_textrmlin)- calibrated. To demonstrate the difficulty in designing surrogates to ℓdγ, we show negative calibration results for convex surrogates and quasi-concave conditional risk cases (these gave positive calibration in adversarial setting without reject option). We also empirically argue that Shifted Double Ramp Loss (DRL) and Shifted Double Sigmoid Loss (DSL) satisfy the calibration conditions. Finally, we demonstrate the robustness of shifted DRL and shifted DSL against adversarial perturbations on a synthetically generated dataset.