提出可自适应调整参数的在线回归算法，有效应对函数序列变化。
A hierarchical Vovk-Azoury-Warmuth forecaster with discounting for online regression in RKHS
- 结合随机特征与折扣机制，构建分层自适应算法
- 理论证明动态误差随时间增长为O(T^{2/3}P_T^{1/3})
- 适合需要实时更新且函数变化较平滑的场景
研究在再生核希尔伯特空间（RKHS）中，针对时变函数序列的无约束二次损失在线回归问题。近期，Jacobsen 和 Cutkosky（2024）提出了折扣Vovk-Azoury-Warmuth（DVAW）预测器，在有限维情形下实现最优动态后悔。本文将该方法推广至非参数域，通过融合随机特征近似构建完全自适应的分层算法——H-VAW-D（Hierarchical Vovk-Azoury-Warmuth with Discounting），同时学习折扣因子与随机特征数量。我们证明该算法每轮复杂度为 $O(T ext{ln} T)$，期望动态后悔为 $O(T^{2/3}P_T^{1/3} + ext{sqrt}{T} ext{ln} T)$，其中 $P_T$ 为比较序列的功能路径长度。
原文摘要 · Abstract (English)
We study the problem of online regression with the unconstrained quadratic loss against a time-varying sequence of functions from a Reproducing Kernel Hilbert Space (RKHS). Recently, Jacobsen and Cutkosky (2024) introduced a discounted Vovk-Azoury-Warmuth (DVAW) forecaster that achieves optimal dynamic regret in the finite-dimensional case. In this work, we lift their approach to the non-parametric domain by synthesizing the DVAW framework with a random feature approximation. We propose a fully adaptive, hierarchical algorithm, which we call H-VAW-D (Hierarchical Vovk-Azoury-Warmuth with Discounting), that learns both the discount factor and the number of random features. We prove that this algorithm, which has a per-iteration computational complexity of $O(T\ln T)$, achieves an expected dynamic regret of $O(T^{2/3}P_T^{1/3} + \sqrt{T}\ln T)$, where $P_T$ is the functional path length of a comparator sequence.
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