新算法在梯度被污染时仍能保持低累积误差，适合高鲁棒性在线学习场景。
Unconstrained Robust Online Convex Optimization
- 设计无约束下的抗污染在线优化算法，不依赖污染机制假设。
- 理论证明误差随总污染量和时间平方根增长，且对任意参考点均有效。
- 适用于对抗性干扰或数据错误的实时决策系统，如金融交易、自动驾驶。
本文研究反馈受污染的在线学习问题。学习者仅获得可能被污染的梯度 $ ilde g_t$，而非真实梯度 $g_t$，且不假设污染来源（如异常值、标签错误或恶意攻击）。重点解决无约束情形下，算法需对任意比较点 $u \∈ \&mathbb{R}^d$ 保持低遗憾。现有方法在小污染下即表现极差，而本工作提出算法，在已知 $G \ge \max_t \|g_t\|$ 时，遗憾为 $\|u\|G (\sqrt{T} + k)$，其中 $k$ 为总污染量；当 $G$ 未知时，额外增加 $(\|u\|^2 + G^2)k$ 的惩罚项。
原文摘要 · Abstract (English)
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 $(\|u\|^2+G^2) k$.
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