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Steffen Finck1, Hans-Georg Beyer

  • 1FH Vorarlberg University of Applied Sciences, Austria.

Theoretical Computer Science
|February 28, 2012
PubMed
Summary
This summary is machine-generated.

This study compares evolution strategies and simultaneous perturbation stochastic approximation (SPSA) on noisy optimization problems. Both algorithms perform similarly, with SPSA showing a slight advantage under optimal conditions and moderate noise.

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Area of Science:

  • Optimization Algorithms
  • Computational Mathematics
  • Machine Learning Theory

Background:

  • Comparing algorithm performance requires compatible measures.
  • Evolution strategies analysis was adapted for stochastic approximation.
  • This approach yields simultaneous convergence results for noisy and non-noisy optimization.

Purpose of the Study:

  • To theoretically compare evolution strategies and simultaneous perturbation stochastic approximation (SPSA).
  • To derive optimal step sizes and convergence criteria for SPSA under three noise models.
  • To validate theoretical findings through simulation experiments.

Main Methods:

  • Applied an analysis approach developed for evolution strategies to SPSA.
  • Derived convergence rates, optimal step sizes, and convergence criteria for SPSA.

Related Experiment Videos

  • Conducted simulation experiments to validate theoretical results.
  • Compared SPSA with evolution strategies on a noisy sphere model.

    • Main Results:

    • The analysis approach successfully yielded convergence results for both noisy and non-noisy scenarios.
    • Optimal step sizes and convergence criteria were derived for SPSA under different noise models.
    • Simulation experiments confirmed the theoretical findings.
    • Both SPSA and evolution strategies demonstrated similar performance on the noisy sphere model.

    Conclusions:

    • SPSA offers a slight performance advantage over evolution strategies when optimal settings are employed and noise levels are not excessive.
    • The adapted analysis approach provides a unified framework for studying noisy and non-noisy optimization algorithms.
    • This research offers valuable insights for selecting and tuning algorithms in noisy optimization contexts.