SPSA in noise free optimization

Author

Gerencsér, László ; Vágó, Zsuzsanna

Author_Institution

Comput. & Autom. Inst., Hungarian Acad. of Sci., Budapest, Hungary

Volume

5

fYear

2000

fDate

2000

Firstpage

3284

Abstract

The SPSA (simultaneous perturbation stochastic approximation) method for function minimization developed in Spall (1992) is analyzed for optimization problems without measurement noise. We prove the result that under appropriate technical conditions the estimator sequence converges to the optimum with geometric rate with probability 1. Numerical experiments support the conjecture that the top Lyapunov-exponent defined in terms of the SPSA method is smaller than the Lyapunov-exponent of its deterministic counterpart. We conclude that randomization improves convergence rate while dramatically reducing the number of function evaluations

Keywords

approximation theory; convergence; optimisation; probability; recursive estimation; convergence rate; estimator sequence; function minimization; noise free optimization; randomization; simultaneous perturbation stochastic approximation; top Lyapunov-exponent; Automation; Convergence; Estimation error; Measurement errors; Minimization methods; Noise measurement; Optimization methods; Recursive estimation; Stochastic processes; Stochastic resonance;

fLanguage

English

Publisher

ieee

Conference_Titel

American Control Conference, 2000. Proceedings of the 2000

Conference_Location

Chicago, IL

ISSN

0743-1619

Print_ISBN

0-7803-5519-9

Type

conf

DOI

10.1109/ACC.2000.879172

Filename

879172