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Adaptive initial step size selection for Simultaneous Perturbation Stochastic Approximation.

Keiichi Ito1, Tom Dhaene2

  • 1Ghent University - iMinds, INTEC, Gaston Crommenlaan 8 bus 201, Ledeberg, 9050 Ghent, Belgium ; Noesis Solutions, Gaston Geenslaan 11 B4, 3001 Louvain, Belgium.

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Summary
This summary is machine-generated.

This study introduces an adaptive stepping method to improve Simultaneous Perturbation Stochastics Approximation (SPSA) by automatically adjusting initial step sizes. This enhances reliable objective function reduction and solution convergence in optimization problems.

Keywords:
Direct methodNoisy functionOptimizationParameter estimationStochastic approximation

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Area of Science:

  • Optimization algorithms
  • Numerical analysis
  • Stochastic processes

Background:

  • Simultaneous Perturbation Stochastics Approximation (SPSA) is sensitive to initial step size choices.
  • Large initial step sizes can lead to convergence failures in SPSA.
  • Reliable optimization requires robust step size selection strategies.

Purpose of the Study:

  • To develop an adaptive stepping method for SPSA.
  • To improve the reliability of objective function reduction in SPSA.
  • To enhance the convergence properties of SPSA, particularly in noisy environments.

Main Methods:

  • An adaptive stepping algorithm was proposed to automatically adjust initial step sizes in SPSA.
  • The method was tested on ten diverse mathematical functions.
  • Three distinct noise levels were applied to evaluate performance robustness.
  • A parameter estimation problem for a nonlinear dynamical system was used as a practical application.

Main Results:

  • The proposed adaptive method demonstrated improved reliability in reducing objective function values.
  • Empirical results across various functions and noise levels validated the effectiveness of the adaptive approach.
  • The method showed promise in handling parameter estimation for complex systems.

Conclusions:

  • The adaptive stepping method offers a more robust alternative to standard SPSA by mitigating sensitivity to initial step sizes.
  • This approach enhances the practical applicability of SPSA in optimization and parameter estimation tasks.
  • Further research could explore extensions to more complex dynamical systems and optimization landscapes.