Decentralized Online Learning with Kernels

TL;DR

This paper introduces a decentralized online learning algorithm for multi-agent systems using kernels, enabling agents to learn near-optimal decision functions through local data and message passing, with proven convergence and practical effectiveness.

Contribution

It proposes a novel decentralized kernel-based online learning method with consensus constraints and low-dimensional projections, improving scalability and convergence in multi-agent settings.

Findings

Convergence to a neighborhood of the global optimum with constant step-size.

Finite complexity of learned functions is guaranteed.

Achieves state-of-the-art performance in distributed multi-class classification.

Abstract

We consider multi-agent stochastic optimization problems over reproducing kernel Hilbert spaces (RKHS). In this setting, a network of interconnected agents aims to learn decision functions, i.e., nonlinear statistical models, that are optimal in terms of a global convex functional that aggregates data across the network, with only access to locally and sequentially observed samples. We propose solving this problem by allowing each agent to learn a local regression function while enforcing consensus constraints. We use a penalized variant of functional stochastic gradient descent operating simultaneously with low-dimensional subspace projections. These subspaces are constructed greedily by applying orthogonal matching pursuit to the sequence of kernel dictionaries and weights. By tuning the projection-induced bias, we propose an algorithm that allows for each individual agent to learn, based upon its locally observed data stream and message passing with its neighbors only, a regression function that is close to the globally optimal regression function. That is, we establish that with constant step-size selections agents' functions converge to a neighborhood of the globally optimal one while satisfying the consensus constraints as the penalty parameter is increased. Moreover, the complexity of the learned regression functions is guaranteed to remain finite. On both multi-class kernel logistic regression and multi-class kernel support vector classification with data generated from class-dependent Gaussian mixture models, we observe stable function estimation and state of the art performance for distributed online multi-class classification. Experiments on the Brodatz textures further substantiate the empirical validity of this approach.