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Gaussian Adaptation as a unifying framework for continuous black-box optimization and adaptive Monte Carlo sampling


Müller, Christian L; Sbalzarini, Ivo F (2010). Gaussian Adaptation as a unifying framework for continuous black-box optimization and adaptive Monte Carlo sampling. In: 2010 IEEE Congress on Evolutionary Computation (CEC), Barcelona, Spain, 18 July 2010 - 23 July 2010, 1-8.

Abstract

We present a unifying framework for continuous optimization and sampling. This framework is based on Gaussian Adaptation (GaA), a search heuristic developed in the late 1960's. It is a maximum-entropy method that shares several features with the (1+1)-variant of the Covariance Matrix Adaptation Evolution Strategy (CMA-ES). The algorithm samples single candidate solutions from a multivariate normal distribution and continuously adapts the first and second moments. We present modifications that turn the algorithm into both a robust continuous black-box optimizer and, alternatively, an adaptive Random Walk Monte Carlo sampler. In black-box optimization, sample-point selection is controlled by a monotonically decreasing, fitness-dependent acceptance threshold. We provide general strategy parameter settings, stopping criteria, and restart mechanisms that render GaA quasi parameter free. We also introduce Metropolis GaA (M-GaA), where sample-point selection is based on the Metropolis acceptance criterion. This turns GaA into a Monte Carlo sampler that is conceptually similar to the seminal Adaptive Proposal (AP) algorithm. We evaluate the performance of Restart GaA on the CEC 2005 benchmark suite. Moreover, we compare the efficacy of M-GaA to that of the Metropolis-Hastings and AP algorithms on selected target distributions.

We present a unifying framework for continuous optimization and sampling. This framework is based on Gaussian Adaptation (GaA), a search heuristic developed in the late 1960's. It is a maximum-entropy method that shares several features with the (1+1)-variant of the Covariance Matrix Adaptation Evolution Strategy (CMA-ES). The algorithm samples single candidate solutions from a multivariate normal distribution and continuously adapts the first and second moments. We present modifications that turn the algorithm into both a robust continuous black-box optimizer and, alternatively, an adaptive Random Walk Monte Carlo sampler. In black-box optimization, sample-point selection is controlled by a monotonically decreasing, fitness-dependent acceptance threshold. We provide general strategy parameter settings, stopping criteria, and restart mechanisms that render GaA quasi parameter free. We also introduce Metropolis GaA (M-GaA), where sample-point selection is based on the Metropolis acceptance criterion. This turns GaA into a Monte Carlo sampler that is conceptually similar to the seminal Adaptive Proposal (AP) algorithm. We evaluate the performance of Restart GaA on the CEC 2005 benchmark suite. Moreover, we compare the efficacy of M-GaA to that of the Metropolis-Hastings and AP algorithms on selected target distributions.

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Additional indexing

Item Type:Conference or Workshop Item (Paper), refereed, original work
Communities & Collections:Special Collections > SystemsX.ch
Special Collections > SystemsX.ch > Research, Technology and Development Projects > WingX
Dewey Decimal Classification:570 Life sciences; biology
Language:English
Event End Date:23 July 2010
Deposited On:05 Jul 2013 11:55
Last Modified:05 Apr 2016 16:51
Publisher DOI:https://doi.org/10.1109/CEC.2010.5586491
Permanent URL: https://doi.org/10.5167/uzh-79215

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