# LEARN: An Invex Loss for Outlier Oblivious Robust Online Optimization

arXiv: https://arxiv.org/abs/2408.06297 · HTML: https://mlsanity.com/paper/2408.06297/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 29 references that are in the map.
- First posted on arXiv 12 Aug 2024.

## Builds on (most cited first, 15 of 15)

- [Introduction to Online Convex Optimization](https://mlsanity.com/paper/1909.05207/) (2019)
- [Online Learning: A Modern Introduction Using Convex Optimization](https://mlsanity.com/paper/1912.13213/) (2019)
- [A General and Adaptive Robust Loss Function](https://mlsanity.com/paper/1701.03077/) (2017)
- [Adaptive Online Learning in Dynamic Environments](https://mlsanity.com/paper/1810.10815/) (2018)
- [Improved Dynamic Regret for Non-degenerate Functions](https://mlsanity.com/paper/1608.03933/) (2016)
- [Generalized Huber Loss for Robust Learning and its Efficient Minimization for a Robust Statistics](https://mlsanity.com/paper/2108.12627/) (2021)
- [Online and Distribution-Free Robustness: Regression and Contextual Bandits with Huber Contamination](https://mlsanity.com/paper/2010.04157/) (2020)
- [Unconstrained Online Learning with Unbounded Losses](https://mlsanity.com/paper/2306.04923/) (2023)
- [Robust Optimization for Deep Regression](https://mlsanity.com/paper/1505.06606/) (2015)
- [Real-time Event Detection on Social Data Streams](https://mlsanity.com/paper/1907.11229/) (2019)
- [Streaming Algorithms for High-Dimensional Robust Statistics](https://mlsanity.com/paper/2204.12399/) (2022)
- [Robust Online Convex Optimization in the Presence of Outliers](https://mlsanity.com/paper/2107.01881/) (2021)
- [Minimum Distance Estimation for Robust High-Dimensional Regression](https://mlsanity.com/paper/1307.3227/) (2013)
- [Outlier Robust Online Learning](https://mlsanity.com/paper/1701.00251/) (2017)
- [Real Time Analytics: Algorithms and Systems](https://mlsanity.com/paper/1708.02621/) (2017)

## Abstract (arXiv)

We study a robust online convex optimization framework, where an adversary can introduce outliers by corrupting loss functions in an arbitrary number of rounds k, unknown to the learner. Our focus is on a novel setting allowing unbounded domains and large gradients for the losses without relying on a Lipschitz assumption. We introduce the Log Exponential Adjusted Robust and iNvex (LEARN) loss, a non-convex (invex) robust loss function to mitigate the effects of outliers and develop a robust variant of the online gradient descent algorithm by leveraging the LEARN loss. We establish tight regret guarantees (up to constants), in a dynamic setting, with respect to the uncorrupted rounds and conduct experiments to validate our theory. Furthermore, we present a unified analysis framework for developing online optimization algorithms for non-convex (invex) losses, utilizing it to provide regret bounds with respect to the LEARN loss, which may be of independent interest.