Multikernel Passive Stochastic Gradient Algorithms and Transfer Learning

This article 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...

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Bibliographic Details
Published in:IEEE transactions on automatic control Vol. 67; no. 4; pp. 1792 - 1805
Main Authors: Krishnamurthy, Vikram, Yin, George
Format: Journal Article
Language:English
Published: New York IEEE 01.04.2022
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Approximation algorithms
Bernstein von-Mises theorem
Convergence
Cost function
Kernel
Least mean squares
Least mean squares algorithm
Machine learning
Monte Carlo methods
Noise measurement
Ordinary differential equations
passive least mean squares (LMS)
stochastic gradient algorithm
stochastic sampling
Transfer learning
Variance analysis
variance reduction
weak convergence
ISSN:0018-9286, 1558-2523
Online Access:Get full text
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Summary:This article 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 article, we construct a multikernel passive stochastic gradient algorithm. The algorithm performs substantially better in high dimensional problems and incorporates variance reduction. We analyze the weak convergence of the multikernel algorithm and its rate of convergence. In numerical examples, we study the multikernel version of the passive least mean squares algorithm for transfer learning to compare the performance with the classical passive version.
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ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2021.3079280