提出新算法VAW²，实现在线多核学习的高效预测。
Random feature-based double Vovk-Azoury-Warmuth algorithm for online multi-kernel learning
- 两级结构：先用随机傅里叶特征生成专家策略，再用VAW方法融合预测。
- 理论证明：期望遗憾界为O(T^{1/2} ln T)，需随机特征数为T^{1/2}。
- 实测表现优：在多个基准数据集上超越Raker、OMKL-GF等主流方法。
我们提出一种新型在线多核学习算法VAW²，用于再生核希尔伯特空间中的在线最小二乘回归。VAW²采用基于随机傅里叶特征的功能逼近，并在两层框架中应用Vovk-Azoury-Warmuth（VAW）方法：第一层对每个核生成的随机特征构建专家策略，第二层再次使用VAW方法组合这些预测。理论分析表明，当随机特征数量为T^{1/2}时，其期望遗憾界为O(T^{1/2} ln T)，依赖于人工随机性。在多个基准数据集上的实验结果表明，VAW²在性能上显著优于现有在线多核学习算法Raker和OMKL-GF，以及其它基于凸组合的理论方法。
原文摘要 · Abstract (English)
We introduce a novel multi-kernel learning algorithm, VAW$^2$, for online least squares regression in reproducing kernel Hilbert spaces (RKHS). VAW$^2$ leverages random Fourier feature-based functional approximation and the Vovk-Azoury-Warmuth (VAW) method in a two-level procedure: VAW is used to construct expert strategies from random features generated for each kernel at the first level, and then again to combine their predictions at the second level. A theoretical analysis yields a regret bound of $O(T^{1/2}\ln T)$ in expectation with respect to artificial randomness, when the number of random features scales as $T^{1/2}$. Empirical results on some benchmark datasets demonstrate that VAW$^2$ achieves superior performance compared to the existing online multi-kernel learning algorithms: Raker and OMKL-GF, and to other theoretically grounded method methods involving convex combination of expert predictions at the second level.
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