Adapting the Covariance Matrix in Evolution Strategies
Silja Meyer-Nieberg, Erik Kropat
2014
Abstract
Evolution strategies belong to the best performing modern natural computing methods for continuous optimization. This paper addresses the covariance matrix adaptation which is central to the algorithm. Nearly all approaches so far consider the sample covariance as one of the main factors for the adaptation. However, as known from modern statistics, this estimate may be of poor quality in many cases. Unfortunately, these cases are encountered often in practical applications. This paper explores the use of different previously unexplored estimates.
References
- Audet, C. (2013). A survey on direct search methods for blackbox optimization and their applications. In Mathematics without boundaries: Surveys in interdisciplinary research. Springer. To appear. Also Les Cahiers du GERAD G-2012-53, 2012.
- Bai, Z. D. and Silverstein, J. W. (1998). No eigenvalues outside the support of the limiting spectral distribution of large-dimensional sample covariance matrices. The Annals of Probability, 26(1):316-345.
- Beyer, H.-G. (2001). The Theory of Evolution Strategies. Natural Computing Series. Springer, Heidelberg.
- Beyer, H.-G. and Meyer-Nieberg, S. (2006). Self-adaptation of evolution strategies under noisy fitness evaluations. Genetic Programming and Evolvable Machines, 7(4):295-328.
- Beyer, H.-G. and Schwefel, H.-P. (2002). Evolution strategies: A comprehensive introduction. Natural Computing, 1(1):3-52.
- Beyer, H.-G. and Sendhoff, B. (2008). Covariance matrix adaptation revisited - the CMSA evolution strategy -. In Rudolph, G. et al., editors, PPSN, volume 5199 of Lecture Notes in Computer Science, pages 123-132. Springer.
- Chen, X., Wang, Z., and McKeown, M. (2012). Shrinkageto-tapering estimation of large covariance matrices. Signal Processing, IEEE Transactions on, 60(11):5640-5656.
- Chen, Y., Wiesel, A., Eldar, Y. C., and Hero, A. O. (2010). Shrinkage algorithms for MMSE covariance estimation. IEEE Transactions on Signal Processing, 58(10):5016-5029.
- Conn, A. R., Scheinberg, K., and Vicente, L. N. (2009). Introduction to Derivative-Free Optimization. MOSSIAM Series on Optimization. SIAM.
- Dong, W. and Yao, X. (2007). Covariance matrix repairing in gaussian based EDAs. In Evolutionary Computation, 2007. CEC 2007. IEEE Congress on, pages 415-422.
- Eiben, A. E. and Smith, J. E. (2003). Introduction to Evolutionary Computing. Natural Computing Series. Springer, Berlin.
- Finck, S., Hansen, N., Ros, R., and Auger, A. (2010). Real-parameter black-box optimization benchmarking 2010: Presentation of the noiseless functions. Technical report, Institute National de Recherche en Informatique et Automatique. 2009/22.
- Fisher, T. J. and Sun, X. (2011). Improved Stein-type shrinkage estimators for the high-dimensional multivariate normal covariance matrix. Computational Statistics & Data Analysis, 55(5):1909 - 1918.
- Hansen, N. (2006). The CMA evolution strategy: A comparing review. In Lozano, J. et al., editors, Towards a new evolutionary computation. Advances in estimation of distribution algorithms, pages 75-102. Springer.
- Hansen, N., Auger, A., Finck, S., and Ros, R. (2012). Real-parameter black-box optimization benchmarking 2012: Experimental setup. Technical report, INRIA.
- Hansen, N., Auger, A., Ros, R., Finck, S., and Pos?ík, P. (2010). Comparing results of 31 algorithms from the black-box optimization benchmarking BBOB-2009. In Proceedings of the 12th annual conference companion on Genetic and evolutionary computation, GECCO 7810, pages 1689-1696, New York, NY, USA. ACM.
- Hansen, N. and Ostermeier, A. (2001). Completely derandomized self-adaptation in evolution strategies. Evolutionary Computation, 9(2):159-195.
- Huber, P. J. (1981). Robust Statistics. Wiley, New York.
- Ledoit, O. and Wolf, M. (2004). A well-conditioned estimator for large dimensional covariance matrices. Journal of Multivariate Analysis Archive, 88(2):265-411.
- Ledoit, O. and Wolf, M. (2012). Non-linear shrinkage estimation of large dimensional covariance matrices. The Annals of Statistics, 40(2):1024-1060.
- Meyer-Nieberg, S. and Beyer, H.-G. (2007). Self-adaptation in evolutionary algorithms. In Lobo, F., Lima, C., and Michalewicz, Z., editors, Parameter Setting in Evolutionary Algorithms, pages 47-76. Springer Verlag, Heidelberg.
- Rechenberg, I. (1973). Evolutionsstrategie: Optimierung technischer Systeme nach Prinzipien der biologischen Evolution. Frommann-Holzboog Verlag, Stuttgart.
- Schäffer, J. and Strimmer, K. (2005). A shrinkage approach to large-scale covariance matrix estimation and implications for functional genomics,. Statistical Applications in Genetics and Molecular Biology, 4(1):Article 32.
- Schwefel, H.-P. (1981). Numerical Optimization of Computer Models. Wiley, Chichester.
- Stein, C. (1956). Inadmissibility of the usual estimator for the mean of a multivariate distribution. In Proc. 3rd Berkeley Symp. Math. Statist. Prob. 1, pages 197-206. Berkeley, CA.
- Stein, C. (1975). Estimation of a covariance matrix. In Rietz Lecture, 39th Annual Meeting. IMS, Atlanta, GA.
- Thomaz, C. E., Gillies, D., and Feitosa, R. (2004). A new covariance estimate for bayesian classifiers in biometric recognition. Circuits and Systems for Video Technology, IEEE Transactions on, 14(2):214-223.
Paper Citation
in Harvard Style
Meyer-Nieberg S. and Kropat E. (2014). Adapting the Covariance Matrix in Evolution Strategies . In Proceedings of the 3rd International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES, ISBN 978-989-758-017-8, pages 89-99. DOI: 10.5220/0004832300890099
in Bibtex Style
@conference{icores14,
author={Silja Meyer-Nieberg and Erik Kropat},
title={Adapting the Covariance Matrix in Evolution Strategies},
booktitle={Proceedings of the 3rd International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,},
year={2014},
pages={89-99},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0004832300890099},
isbn={978-989-758-017-8},
}
in EndNote Style
TY - CONF
JO - Proceedings of the 3rd International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,
TI - Adapting the Covariance Matrix in Evolution Strategies
SN - 978-989-758-017-8
AU - Meyer-Nieberg S.
AU - Kropat E.
PY - 2014
SP - 89
EP - 99
DO - 10.5220/0004832300890099