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Conference Papers Year : 2018

A Comparative Study of Large-scale Variants of CMA-ES

Konstantinos Varelas
Anne Auger
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  • PersonId : 751513
  • IdHAL : anne-auger
Dimo Brockhoff
Nikolaus Hansen
Yann Semet
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  • PersonId : 830846
Frédéric Barbaresco

Abstract

The CMA-ES is one of the most powerful stochastic numerical optimizers to address difficult black-box problems. Its intrinsic time and space complexity is quadratic-limiting its applicability with increasing problem dimensionality. To circumvent this limitation, different large-scale variants of CMA-ES with subquadratic complexity have been proposed over the past ten years. To-date however, these variants have been tested and compared only in rather restrictive settings, due to the lack of a comprehensive large-scale testbed to assess their performance. In this context, we introduce a new large-scale testbed with dimension up to 640, implemented within the COCO benchmarking platform. We use this testbed to assess the performance of several promising variants of CMA-ES and the standard limited-memory L-BFGS. In all tested dimensions, the best CMA-ES variant solves more problems than L-BFGS for larger budgets while L-BFGS outperforms the best CMA-ES variant for smaller budgets. However, over all functions, the cumulative runtime distributions between L-BFGS and the best CMA-ES variants are close (less than a factor of 4 in high dimension). Our results illustrate different scaling behaviors of the methods, expose a few defects of the algorithms and reveal that for dimension larger than 80, LM-CMA solves more problems than VkD-CMA while in the cumulative runtime distribution over all functions the VkD-CMA dominates or shows almost equal success rate with LM-CMA for budgets up to 10 4 times dimension and for all budgets up to dimension 80.
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Dates and versions

hal-01881454 , version 1 (26-09-2018)
hal-01881454 , version 2 (09-06-2020)

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Konstantinos Varelas, Anne Auger, Dimo Brockhoff, Nikolaus Hansen, Ouassim Ait Elhara, et al.. A Comparative Study of Large-scale Variants of CMA-ES. PPSN XV 2018 - 15th International Conference on Parallel Problem Solving from Nature, Sep 2018, Coimbra, Portugal. pp.3-15, ⟨10.1007/978-3-319-99253-2_1⟩. ⟨hal-01881454v2⟩
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