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Main Authors: Zhang, Jiujia, Cutkosky, Ashok
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2506.12781
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author Zhang, Jiujia
Cutkosky, Ashok
author_facet Zhang, Jiujia
Cutkosky, Ashok
contents This paper addresses online learning with ``corrupted'' feedback. Our learner is provided with potentially corrupted gradients $\tilde g_t$ instead of the ``true'' gradients $g_t$. 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 $u \in \mathbb{R}^d$. 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 (\sqrt{T} + k) $ when $G \ge \max_t \|g_t\|$ is known, where $k$ is a measure of the total amount of corruption. When $G$ is unknown we incur an extra additive penalty of $(\|u\|^2+G^2) k$.
format Preprint
id arxiv_https___arxiv_org_abs_2506_12781
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Unconstrained Robust Online Convex Optimization
Zhang, Jiujia
Cutkosky, Ashok
Machine Learning
Optimization and Control
This paper addresses online learning with ``corrupted'' feedback. Our learner is provided with potentially corrupted gradients $\tilde g_t$ instead of the ``true'' gradients $g_t$. 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 $u \in \mathbb{R}^d$. 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 (\sqrt{T} + k) $ when $G \ge \max_t \|g_t\|$ is known, where $k$ is a measure of the total amount of corruption. When $G$ is unknown we incur an extra additive penalty of $(\|u\|^2+G^2) k$.
title Unconstrained Robust Online Convex Optimization
topic Machine Learning
Optimization and Control
url https://arxiv.org/abs/2506.12781