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Summary: Two-Timescale Simultaneous Perturbation
Stochastic Approximation Using
Deterministic Perturbation Sequences
SHALABH BHATNAGAR
Indian Institute of Science, Bangalore
MICHAEL C. FU and STEVEN I. MARCUS
University of Maryland, College Park, Maryland
and
I-JENG WANG
Johns Hopkins University, Applied Physics Laboratory, Laurel, Maryland
Simultaneous perturbation stochastic approximation (SPSA) algorithms have been found to be very
effective for high-dimensional simulation optimization problems. The main idea is to estimate the
gradient using simulation output performance measures at only two settings of the N-dimensional
parameter vector being optimized rather than at the N + 1 or 2N settings required by the usual
one-sided or symmetric difference estimates, respectively. The two settings of the parameter vec-
tor are obtained by simultaneously changing the parameter vector in each component direction
using random perturbations. In this article, in order to enhance the convergence of these algo-
rithms, we consider deterministic sequences of perturbations for two-timescale SPSA algorithms.
Two constructions for the perturbation sequences are considered: complete lexicographical cycles
and much shorter sequences based on normalized Hadamard matrices. Recently, one-simulation
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