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

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.

DOI: 10.1145/1830483.1830563

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Cite this paper

@inproceedings{Shir2010ForcedOC, title={Forced optimal covariance adaptive learning: modified CMA-ES for efficient hessian determination}, author={Ofer M. Shir and Jonathan Roslund and Herschel Rabitz}, booktitle={GECCO}, year={2010} }