Improved Kernel Alignment Regret Bound for Online Kernel Learning
Junfan LiShizhong Liao
Junfan LiShizhong Liao
Dec 2022
0被引用
15笔记
读论文，拿好礼活动火爆进行中，iPad、蓝牙耳机、拍立得、键盘鼠标套装等你来拿！
摘要原文
In this paper, we improve the kernel alignment regret bound for online kernellearning in the regime of the Hinge loss function. Previous algorithm achievesa regret of $O((\mathcal{A}_TT\ln{T})^{\frac{1}{4}})$ at a computationalcomplexity (space and per-round time) of $O(\sqrt{\mathcal{A}_TT\ln{T}})$,where $\mathcal{A}_T$ is called \textit{kernel alignment}. We propose analgorithm whose regret bound and computational complexity are better thanprevious results. Our results depend on the decay rate of eigenvalues of thekernel matrix. If the eigenvalues of the kernel matrix decay exponentially,then our algorithm enjoys a regret of $O(\sqrt{\mathcal{A}_T})$ at acomputational complexity of $O(\ln^2{T})$. Otherwise, our algorithm enjoys aregret of $O((\mathcal{A}_TT)^{\frac{1}{4}})$ at a computational complexity of$O(\sqrt{\mathcal{A}_TT})$. We extend our algorithm to batch learning andobtain a $O(\frac{1}{T}\sqrt{\mathbb{E}[\mathcal{A}_T]})$ excess risk boundwhich improves the previous $O(1/\sqrt{T})$ bound.
