Random Directions Stochastic Approximation with Deterministic Perturbations

Prashanth, LA and Bhatnagar, S and Bhavsar, N and Fu, M and Marcus, SI (2020) Random Directions Stochastic Approximation with Deterministic Perturbations. In: IEEE Transactions on Automatic Control, 65 (6). pp. 2450-2465.

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Abstract

We introduce deterministic perturbation (DP) schemes for the recently proposed random directions stochastic approximation, and propose new first-order and second-order algorithms. In the latter case, these are the first second-order algorithms to incorporate DPs. We show that the gradient and/or Hessian estimates in the resulting algorithms with DPs are asymptotically unbiased, so that the algorithms are provably convergent. Furthermore, we derive convergence rates to establish the superiority of the first-order and second-order algorithms, for the special case of a convex and quadratic optimization problem, respectively. Numerical experiments are used to validate the theoretical results. © 1963-2012 IEEE.

Item Type:	Journal Article
Publication:	IEEE Transactions on Automatic Control
Publisher:	Institute of Electrical and Electronics Engineers Inc.
Additional Information:	Copy right for this article belongs to Institute of Electrical and Electronics Engineers Inc.
Keywords:	Approximation theory; Quadratic programming; Stochastic systems, Convergence rates; Deterministic perturbation; First order; Numerical experiments; Quadratic optimization problems; Second-order algorithms; Stochastic approximations, Approximation algorithms
Department/Centre:	Division of Electrical Sciences > Computer Science & Automation Division of Interdisciplinary Sciences > Robert Bosch Centre for Cyber Physical Systems
Date Deposited:	10 Nov 2020 07:34
Last Modified:	10 Nov 2020 07:34
URI:	http://eprints.iisc.ac.in/id/eprint/65718

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