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Activity Number:
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522
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Type:
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Contributed
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Date/Time:
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Wednesday, August 5, 2009 : 2:00 PM to 3:50 PM
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Sponsor:
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Section on Statistical Computing
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| Abstract - #304579 |
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Title:
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Stochastic Root-Finding and Optimization via the Adaptive Simultaneous Perturbation Algorithm
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Author(s):
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James C. Spall*+
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Companies:
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Johns Hopkins University Applied Physics Laboratory
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Address:
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, Laurel, MD, 20723-6099,
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Keywords:
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stochastic optimization ; adaptive estimation ; simultaneous perturbation stochastic approximation (SPSA) ; root finding ; stochastic search ; Hessian matrix
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Abstract:
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Consider the problem of root-finding and/or optimization in the presence of noisy function measurements. It is known that a stochastic approximation (SA) analogue of the deterministic Newton-Raphson algorithm provides an asymptotically optimal or near-optimal form of stochastic search. However, directly determining the required Jacobian matrix (or Hessian matrix for optimization) is difficult or impossible in practice. This paper presents a general adaptive SA algorithm that is based on a simple simultaneous perturbation method for estimating the Jacobian matrix while concurrently estimating the primary parameters of interest. From the use of simultaneous perturbations, the algorithm requires only a small number of loss function or gradient measurements per iteration---independent of the problem dimension---to adaptively estimate the Jacobian matrix and parameters of primary interest.
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