Random feature-based double Vovk-Azoury-Warmuth algorithm for online multi-kernel learning

2025-03-25

AI Summary

This paper addresses least-squares regression in online multi-kernel learning. We propose a novel two-layer Vovk–Azoury–Warmuth (VAW) framework: the first layer constructs randomized Fourier feature mappings for each kernel to generate expert predictors; the second layer dynamically aggregates these experts’ outputs via time-varying weights. To our knowledge, this is the first work to hierarchically integrate randomized features with the VAW algorithm for online multi-kernel learning. Under a reproducing kernel Hilbert space (RKHS) formulation, we jointly optimize both the multi-kernel combination weights and the feature mappings, establishing an expected regret bound of $O(sqrt{T} log T)$. Extensive experiments on multiple benchmark datasets demonstrate that our method significantly outperforms state-of-the-art online multi-kernel algorithms—including Raker and OMKL-GF—validating both the tightness of the theoretical bound and the practical efficacy of the approach.

Technology Category

• Machine Learning: Kernel Methods
• Search and Optimization: Learning to Search
• Multiagent Systems: Multiagent Learning

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs

Abstract

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.

Problem

• Online multi-kernel learning for least squares regression
• Random feature-based functional approximation in RKHS
• Regret bound analysis and empirical performance comparison

Innovation

• Random Fourier feature-based functional approximation
• Two-level Vovk-Azoury-Warmuth procedure
• Online multi-kernel learning with regret bound