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Learning Step-Size Adaptation in CMA-ES

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Parallel Problem Solving from Nature – PPSN XVI (PPSN 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12269))

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Abstract

An algorithm’s parameter setting often affects its ability to solve a given problem, e.g., population-size, mutation-rate or crossover-rate of an evolutionary algorithm. Furthermore, some parameters have to be adjusted dynamically, such as lowering the mutation-strength over time. While hand-crafted heuristics offer a way to fine-tune and dynamically configure these parameters, their design is tedious, time-consuming and typically involves analyzing the algorithm’s behavior on simple problems that may not be representative for those that arise in practice. In this paper, we show that formulating dynamic algorithm configuration as a reinforcement learning problem allows us to automatically learn policies that can dynamically configure the mutation step-size parameter of Covariance Matrix Adaptation Evolution Strategy (CMA-ES). We evaluate our approach on a wide range of black-box optimization problems, and show that (i) learning step-size policies has the potential to improve the performance of CMA-ES; (ii) learned step-size policies can outperform the default Cumulative Step-Size Adaptation of CMA-ES; and transferring the policies to (iii) different function classes and to (iv) higher dimensions is also possible.

G. Shala and A. Biedenkapp—Equal Contribution.

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Notes

  1. 1.

    We assume that the cost function is well-defined such that an optimal policy exists.

  2. 2.

    When such a long history is not available yet, the missing values are filled with zeros.

  3. 3.

    Code and trained policies available at https://github.com/automl/LTO-CMA.

  4. 4.

    https://ml.informatik.uni-freiburg.de/papers/20-PPSN-LTO-CMA.pdf.

  5. 5.

    Estimates \(\ge 0.64\) \(\implies \) our learned policy significantly outperformed CSA (\(\alpha \,{=}\,0.05\)).

  6. 6.

    The learned policies outperform CSA on anytime performance as shown in the Appendix, but CSA is better in terms of end objective values.

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Acknowledgements

The authors acknowledge funding by the Robert Bosch GmbH.

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Authors and Affiliations

  1. University of Freiburg, Freiburg im Breisgau, Germany

    Gresa Shala, André Biedenkapp, Noor Awad, Steven Adriaensen & Frank Hutter

  2. Leibniz University Hannover, Hanover, Germany

    Marius Lindauer

  3. Bosch Center for Artificial Intelligence, Renningen, Germany

    Frank Hutter

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  1. Gresa Shala
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  2. André Biedenkapp
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  4. Steven Adriaensen
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Correspondence to André Biedenkapp .

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Editors and Affiliations

  1. Leiden University, Leiden, The Netherlands

    Thomas Bäck

  2. Leiden University, Leiden, The Netherlands

    Mike Preuss

  3. Leiden University, Leiden, The Netherlands

    André Deutz

  4. Sorbonne University, Paris, France

    Hao Wang

  5. Sorbonne University, Paris, France

    Carola Doerr

  6. Leiden University, Leiden, The Netherlands

    Michael Emmerich

  7. University of Münster, Münster, Germany

    Heike Trautmann

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Shala, G., Biedenkapp, A., Awad, N., Adriaensen, S., Lindauer, M., Hutter, F. (2020). Learning Step-Size Adaptation in CMA-ES. In: Bäck, T., et al. Parallel Problem Solving from Nature – PPSN XVI. PPSN 2020. Lecture Notes in Computer Science(), vol 12269. Springer, Cham. https://doi.org/10.1007/978-3-030-58112-1_48

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