Simultaneous Perturbation and Finite Difference Methods

Bhatnagar, Shalabh

doi:10.1002/9780470400531.eorms0784

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Methodology 21 Problem Formulation1

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2011

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Cited by 2 publications

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“…The stochastic optimization algorithm for solving (1) is given by the following iterative scheme: (2) where ˆk  is the estimate of θ at iteration k and ˆ( )…”

Section: Methodology 21 Problem Formulationmentioning

confidence: 99%

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Preliminary results on non-bernoulli distribution of perturbations for simultaneous perturbation stochastic approximation

Cao

2011

Proceedings of the 2011 American Control Conference

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Simultaneous perturbation stochastic approximation (SPSA) has proven to be an efficient algorithm for recursive optimization. SPSA uses a centered difference approximation to the gradient based on only two function evaluations regardless of the dimension of the problem. Typically, the Bernoulli ±1 distribution is used for perturbation vectors and theory has been established to prove the asymptotic optimality of this distribution. However, efficiency of the Bernoulli distribution may not be guaranteed for small-samples. In this paper, we investigate the performance of segmented uniform distribution for perturbation vectors. For smallsamples, we show that the Bernoulli distribution may not be the best for a certain choice of parameters.

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“…The stochastic optimization algorithm for solving (1) is given by the following iterative scheme: (2) where ˆk  is the estimate of θ at iteration k and ˆ( )…”

Section: Methodology 21 Problem Formulationmentioning

confidence: 99%

“…It has wide applications in engineering such as signal processing, system identification and parameter estimation (see www.jhuapl.edu/SPSA and [2,9]). …”

Section: Introductonmentioning

confidence: 99%