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A hierarchical Vovk-Azoury-Warmuth forecaster with discounting for online regression in RKHS

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arxiv 2506.22631 v1 pith:XODPUIHC submitted 2025-06-27 cs.LG stat.ML

A hierarchical Vovk-Azoury-Warmuth forecaster with discounting for online regression in RKHS

classification cs.LG stat.ML
keywords hierarchicalvovk-azoury-warmuthachievesalgorithmdiscountingdvawdynamicforecaster
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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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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  1. Dynamic Regret for Online Regression in RKHS via Discounted VAW and Subspace Approximation

    cs.LG 2026-04 unverdicted novelty 7.0

    Dynamic regret bounds for online kernel regression are obtained by running ensembles of discounted VAW forecasters on orthogonal subspace approximations of the RKHS, with explicit constructions for Gaussian, analytic,...