Multi-kernel Passive Stochastic Gradient Algorithms and Transfer Learning

TL;DR

This paper introduces a multi-kernel passive stochastic gradient algorithm that improves performance in high-dimensional problems and includes variance reduction, with theoretical analysis and transfer learning applications.

Contribution

It presents a novel multi-kernel approach for passive stochastic gradients, enhancing efficiency and convergence in high-dimensional settings.

Findings

Better performance in high-dimensional problems

Incorporates variance reduction techniques

Shows improved convergence in numerical examples

Abstract

This paper develops a novel passive stochastic gradient algorithm. In passive stochastic approximation, the stochastic gradient algorithm does not have control over the location where noisy gradients of the cost function are evaluated. Classical passive stochastic gradient algorithms use a kernel that approximates a Dirac delta to weigh the gradients based on how far they are evaluated from the desired point. In this paper we construct a multi-kernel passive stochastic gradient algorithm. The algorithm performs substantially better in high dimensional problems and incorporates variance reduction. We analyze the weak convergence of the multi-kernel algorithm and its rate of convergence. In numerical examples, we study the multi-kernel version of the passive least mean squares (LMS) algorithm for transfer learning to compare the performance with the classical passive version.