# Unconstrained Robust Online Convex Optimization

arXiv: https://arxiv.org/abs/2506.12781 · HTML: https://mlsanity.com/paper/2506.12781/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jun 2025.

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

- [Infinite-Dimensional Operator/Block Kaczmarz Algorithms: Regret Bounds and λ-Effectiveness](https://mlsanity.com/paper/2511.07604/) (2025)
- [Stress-Aware Learning under KL Drift via Trust-Decayed Mirror Descent](https://mlsanity.com/paper/2510.15222/) (2025)
- [Online Conformal Prediction with Corrupted Feedback](https://mlsanity.com/paper/2605.20515/) (2026)

## Abstract (arXiv)

This paper addresses online learning with ``corrupted'' feedback. Our learner is provided with potentially corrupted gradients tilde gt instead of the ``true'' gradients gt. We make no assumptions about how the corruptions arise: they could be the result of outliers, mislabeled data, or even malicious interference. We focus on the difficult ``unconstrained'' setting in which our algorithm must maintain low regret with respect to any comparison point u ∈ ℝd. The unconstrained setting is significantly more challenging as existing algorithms suffer extremely high regret even with very tiny amounts of corruption (which is not true in the case of a bounded domain). Our algorithms guarantee regret  |u|G (√T + k)  when G ≥ maxt |gt| is known, where k is a measure of the total amount of corruption. When G is unknown we incur an extra additive penalty of (|u|2+G2) k.