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Year: 2010

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

Müller, Christian L ; Sbalzarini, Ivo F

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 (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.

DOI: https://doi.org/10.1109/CEC.2010.5586491

Posted at the Zurich Open Repository and Archive, University of Zurich ZORA URL: https://doi.org/10.5167/uzh-79215 Conference or Workshop Item

Originally published at: 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 (CEC), Barcelona, Spain, 18 July 2010 - 23 July 2010, 1-8. DOI: https://doi.org/10.1109/CEC.2010.5586491 Gaussian Adaptation as a unifying framework for continuous black-box optimization and adaptive Monte Carlo sampling

Christian L. Muller,¨ Ivo F. Sbalzarini Institute of Theoretical Computer Science and Swiss Institute of Bioinformatics ETH Zurich, CH-8092 Z¨urich, Switzerland

Abstract— We present a unifying framework for continu- For both problem classes, Monte Carlo methods have ous optimization and sampling. This framework is based on become the prevalent computational paradigm. They rely on Gaussian Adaptation (GaA), a search heuristic developed in iterative random sampling in order to approximate the desired the late 1960’s. It is a maximum-entropy method that shares several features with the (1+1)-variant of the Covariance Ma- result. A crucial design decision is how the random samples trix Adaptation Evolution Strategy (CMA-ES). The algorithm are generated. In continuous spaces, multivariate Gaussian samples single candidate solutions from a multivariate normal distributions are the standard choice. Several continuous distribution and continuously adapts the first and second black-box optimization methods, such as Simulated Anneal- moments. We present modifications that turn the algorithm into ing (SA) in general state spaces [1], Gaussian Adaptation both a robust continuous black-box optimizer and, alternatively, an adaptive Random Walk Monte Carlo sampler. In black-box (GaA) [2], and Evolution Strategies (ES) use Gaussian sam- optimization, sample-point selection is controlled by a monoton- pling to generate candidate solutions. For indirect sampling, ically decreasing, fitness-dependent acceptance threshold. We Green and Han [3] were among the first to employ Gaussian provide general strategy parameter sett