SPSA algorithms with measurement reuse

Abdulla, Mohammed Shahid and Bhatnagar, Shalabh (2006) SPSA algorithms with measurement reuse. In: 2006 Winter Simulation Conference,, Dec 03-06, 2006, Monterey, CA,, pp. 319-327.

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Abstract

Four algorithms, all variants of Simultaneous Perturbation Stochastic Approximation (SPSA), are proposed. The original one-measurement SPSA uses an estimate of the gradient of objective function L containing an additional bias term not seen in two-measurement SPSA. As a result, the asymptotic covariance matrix of the iterate convergence process has a bias term. We propose a one-measurement algorithm that eliminates this bias, and has asymptotic convergence properties making for easier comparison with the two-measurement SPSA. The algorithm, under certain conditions, outperforms both forms of SPSA with the only overhead being the storage of a single measurement. We also propose a similar algorithm that uses perturbations obtained from normalized Hadamard matrices. The convergence w.p. 1 of both algorithms is established. We extend measurement reuse to design two second-order SPSA algorithms and sketch the convergence analysis. Finally, we present simulation results on an illustrative minimization problem.

Item Type:	Conference Paper
Publisher:	Institute of Electrical and Electronics Engineers
Additional Information:	Copyright 2006 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
Department/Centre:	Division of Electrical Sciences > Computer Science & Automation
Date Deposited:	08 Sep 2010 10:08
Last Modified:	22 Feb 2012 06:52
URI:	http://eprints.iisc.ac.in/id/eprint/30532

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