Advertisement

Online Model Selection for Restricted Covariance Matrix Adaptation

  • Youhei AkimotoEmail author
  • Nikolaus Hansen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9921)

Abstract

We focus on a variant of covariance matrix adaptation evolution strategy (CMA-ES) with a restricted covariance matrix model, namely VkD-CMA, which is aimed at reducing the internal time complexity and the adaptation time in terms of function evaluations. We tackle the shortage of the VkD-CMA—the model of the restricted covariance matrices needs to be selected beforehand. We propose a novel mechanism to adapt the model online in the VkD-CMA. It eliminates the need for advance model selection and leads to a performance competitive with or even better than the algorithm with a nearly optimal but fixed model.

Keywords

Covariance Matrix Learning Rate Covariance Model Fast Adaptation Optimal Convergence Rate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

This work is partially supported by JSPS KAKENHI Grant Number 15K16063.

References

  1. 1.
    Akimoto, Y.: Analysis of a natural gradient algorithm on monotonic convex-quadratic-composite functions. In: Proceedings of Genetic and Evolutionary Computation Conference, pp. 1293–1300. ACM (2012)Google Scholar
  2. 2.
    Akimoto, Y., Auger, A., Hansen, N.: Comparison-based natural gradient optimization in high dimension. In: Proceedings of Genetic and Evolutionary Computation Conference, pp. 373–380. ACM (2014)Google Scholar
  3. 3.
    Akimoto, Y., Hansen, N.: Projection-based restricted covariance matrix adaptation for high dimension. In: Proceedings of Genetic and Evolutionary Computation Conference. ACM (2016, to appear)Google Scholar
  4. 4.
    Arnold, D.V.: Optimal weighted recombination. In: Wright, A.H., Vose, M.D., De Jong, K.A., Schmitt, L.M. (eds.) FOGA 2005. LNCS, vol. 3469, pp. 215–237. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  5. 5.
    Hansen, N., Atamna, A., Auger, A.: How to assess step-size adaptation mechanisms in randomised search. In: Bartz-Beielstein, T., Branke, J., Filipič, B., Smith, J. (eds.) PPSN 2014. LNCS, vol. 8672, pp. 60–69. Springer, Heidelberg (2014)Google Scholar
  6. 6.
    Hansen, N., Auger, A.: Principled design of continuous stochastic search: from theory to practice. In: Borenstein, Y., Moraglio, A. (eds.) Theory and Principled Methods for the Design of Metaheuristics. NCS. Springer, Berlin (2014)Google Scholar
  7. 7.
    Hansen, N., Muller, S.D., Koumoutsakos, P.: Reducing the time complexity of the derandomized evolution strategy with covariance matrix adaptation (CMA-ES). Evol. Comput. 11(1), 1–18 (2003)CrossRefGoogle Scholar
  8. 8.
    Hansen, N., Ostermeier, A.: Completely derandomized self-adaptation in evolution strategies. Evol. Comput. 9(2), 159–195 (2001)CrossRefGoogle Scholar
  9. 9.
    Jastrebski, G., Arnold, D.V.: Improving evolution strategies through active covariance matrix adaptation. In: 2006 IEEE Congress on Evolutionary Computation, pp. 9719–9726. IEEE (2006)Google Scholar
  10. 10.
    Loshchilov, I.: A computationally efficient limited memory CMA-ES for large scale optimization. In: Proceedings of Genetic and Evolutionary Computation Conference, pp. 397–404 (2014)Google Scholar
  11. 11.
    Ros, R., Hansen, N.: A simple modification in CMA-ES achieving linear time and space complexity. In: Rudolph, G., Jansen, T., Lucas, S., Poloni, C., Beume, N. (eds.) PPSN 2008. LNCS, vol. 5199, pp. 296–305. Springer, Heidelberg (2008)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  1. 1.Faculty of EngineeringShinshu UniversityNaganoJapan
  2. 2.Inria, Research Centre Saclay – Île-de-FrancePalaiseauFrance

Personalised recommendations