无需预知参数的在线学习算法，性能随梯度变化量优化
Gradient-Variation Regret Bounds for Unconstrained Online Learning
- 基于梯度变化量设计自适应算法，无需事先知道参数
- 在平滑凸损失下实现近似最优的$ ilde{O}( orm{u} oot{V_T(u)} + L orm{u}^2 + G^4)$ regret
- 适用于动态环境与随机-对抗混合模型，适合追求鲁棒性研究者
我们提出了无须参数设定的无约束在线学习算法，其后悔界与梯度变化量 $V_T(u) = \ sum_{t=2}^T \ abla f_t(u)- abla f_{t-1}(u)\ |^2$ 相关。对于 $L$-光滑凸损失，我们设计了完全自适应算法，在无需预先知晓比较器范数 $ orm{u}$、利普希茨常数 $G$ 或光滑性 $L$ 的情况下，达到 $ ilde{O}( orm{u} oot{V_T(u)} + L orm{u}^2 + G^4)$ 的后悔界。每轮更新可通过闭式表达高效计算。该结果可扩展至动态后悔，并对随机-对抗扩展（SEA）模型带来显著改进，优于此前最佳结果（Wang et al., 2025）。
原文摘要 · Abstract (English)
We develop parameter-free algorithms for unconstrained online learning with regret guarantees that scale with the gradient variation $V_T(u) = \sum_{t=2}^T \|\nabla f_t(u)-\nabla f_{t-1}(u)\|^2$. For $L$-smooth convex losses, we provide fully-adaptive algorithms achieving regret of $\widetilde{O}(\|u\|\sqrt{V_T(u)} + L\|u\|^2+G^4)$ without requiring prior knowledge of comparator norm $\|u\|$, Lipschitz constant $G$, or smoothness $L$. The update in each round can be computed efficiently via a closed-form expression. Our results extend to dynamic regret and find immediate implications for the stochastically-extended adversarial (SEA) model, which significantly improves upon the previous best-known result (Wang et al., 2025).
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