[Paper Review] Distributed Online Learning with Multiple Kernels

Jeongmin Chae, Song‐Nam Hong|arXiv (Cornell University)|Feb 25, 2021

Advanced Adaptive Filtering Techniques4 citations

TL;DR

This paper proposes DOMKL, a fully decentralized online learning framework with multiple kernels for streaming data in IoT networks. By combining online ADMM and a distributed Hedge algorithm, DOMKL achieves an optimal ${\cal O}(\sqrt{T})$ regret bound, enabling each node to learn a shared nonlinear function with diminishing error over time while preserving data privacy.

ABSTRACT

We consider the problem of learning a nonlinear function over a network of learners in a fully decentralized fashion. Online learning is additionally assumed, where every learner receives continuous streaming data locally. This learning model is called a fully distributed online learning (or a fully decentralized online federated learning). For this model, we propose a novel learning framework with multiple kernels, which is named DOMKL. The proposed DOMKL is devised by harnessing the principles of an online alternating direction method of multipliers and a distributed Hedge algorithm. We theoretically prove that DOMKL over T time slots can achieve an optimal sublinear regret, implying that every learner in the network can learn a common function which has a diminishing gap from the best function in hindsight. Our analysis also reveals that DOMKL yields the same asymptotic performance of the state-of-the-art centralized approach while keeping local data at edge learners. Via numerical tests with real datasets, we demonstrate the effectiveness of the proposed DOMKL on various online regression and time-series prediction tasks.

Motivation & Objective

• To address the challenge of learning nonlinear functions in a decentralized, privacy-preserving manner with continuous streaming data.
• To develop a distributed online learning framework that supports multiple kernel learning (MKL) without centralizing data.
• To achieve sublinear regret in a fully decentralized network while maintaining local data privacy.
• To extend online kernel learning to distributed settings with scalable, real-time performance.

Proposed method

• DOMKL employs an online alternating direction method of multipliers (ADMM) to coordinate learning across decentralized nodes.
• It integrates a distributed Hedge algorithm to dynamically select the best kernel combination from a predefined dictionary of P kernels.
• The framework uses random feature approximation to reduce computational complexity and enable online updates.
• Each node maintains local estimates of model parameters and dual variables, updating them via consensus and local data.
• The algorithm ensures convergence by enforcing consensus constraints through ADMM and balancing kernel selection via exponential weighting.
• Theoretical analysis proves that the regret grows as ${\cal O}(\sqrt{T})$, matching the performance of centralized online MKL.

Experimental results

Research questions

• RQ1 Can a fully decentralized online learning system achieve sublinear regret in nonlinear function learning with multiple kernels?
• RQ2 How can kernel selection be dynamically optimized in a distributed, privacy-preserving manner under streaming data?
• RQ3 Can the proposed framework match the asymptotic performance of centralized online MKL without data centralization?
• RQ4 What is the impact of network topology and communication constraints on the convergence and regret of distributed online MKL?

Key findings

• DOMKL achieves an optimal sublinear regret of ${\cal O}(\sqrt{T})$ over $T$ time slots, ensuring the learning error diminishes over time.
• The framework matches the asymptotic performance of state-of-the-art centralized online multiple kernel learning methods.
• Numerical evaluations on real datasets confirm DOMKL's effectiveness in online regression and time-series prediction tasks.
• The algorithm maintains local data at edge devices, satisfying strong privacy requirements in IoT applications.
• The regret bound is derived using Hoeffding's inequality and telescoping sum techniques, validating theoretical convergence.
• Parameter tuning, particularly $\eta_g = {\cal O}(\sqrt{T})$, ensures the sublinear regret is achieved.