Forced optimal covariance adaptive learning: Modified CMA-ES for efficient hessian determination

Ofer M. Shir, Jonathan Roslund, Herschel Albert Rabitz

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations

Abstract

Although the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) is commonly believed to evolve a covariance matrix reflective of the underlying search landscape, its deployment on high-dimensional (n ≳ 30) landscapes fails to discover a matrix associated with the well-defined Hessian at the global optimum. After illustrating and explaining this deportment, we introduce a novel technique, entitled Forced Optimal Covariance Adaptive Learning (FOCAL), with the explicit goal of Hessian determination at the global basin of attraction. FOCAL is demonstrated to retrieve the Hessian matrix with high fidelity on both model landscapes and experimental Quantum Control systems, which are observed to possess a non-separable, non-quadratic search landscape. The recovered Hessian forms are corroborated by physical knowledge of the systems and are indeed shown to be local.

Original languageEnglish (US)
Title of host publicationProceedings of the 12th Annual Genetic and Evolutionary Computation Conference, GECCO '10
Pages421-422
Number of pages2
DOIs
StatePublished - Aug 27 2010
Event12th Annual Genetic and Evolutionary Computation Conference, GECCO-2010 - Portland, OR, United States
Duration: Jul 7 2010Jul 11 2010

Publication series

NameProceedings of the 12th Annual Genetic and Evolutionary Computation Conference, GECCO '10

Other

Other12th Annual Genetic and Evolutionary Computation Conference, GECCO-2010
CountryUnited States
CityPortland, OR
Period7/7/107/11/10

All Science Journal Classification (ASJC) codes

  • Computational Theory and Mathematics
  • Theoretical Computer Science

Keywords

  • Experimental optimization
  • FOCAL
  • Hessian learning

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  • Cite this

    Shir, O. M., Roslund, J., & Rabitz, H. A. (2010). Forced optimal covariance adaptive learning: Modified CMA-ES for efficient hessian determination. In Proceedings of the 12th Annual Genetic and Evolutionary Computation Conference, GECCO '10 (pp. 421-422). (Proceedings of the 12th Annual Genetic and Evolutionary Computation Conference, GECCO '10). https://doi.org/10.1145/1830483.1830563