A Simple Modification in CMA-ES Achieving Linear Time and Space Complexity

Raymond Ros (1, 2) , Nikolaus Hansen (1)

1 TANC - Algorithmic number theory for cryptology
2 LRI - Laboratoire de Recherche en Informatique

This report proposes a simple modification of the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) for high dimensional objective functions that reduces the internal time and space complexity from quadratic to linear. The covariance matrix is constrained to be diagonal and the resulting algorithm, sep-CMA-ES, samples each coordinate independently. Because the model complexity is reduced, the learning rate for the covariance matrix can be increased. Consequently, on essentially separable functions, sep-CMA-ES significantly outperforms CMA-ES. For dimension larger than 100, even on the non-separable Rosenbrock function, the sep-CMA-ES needs fewer function evaluations than CMA-ES.

Domains: Numerical Analysis [cs.NA]

Raymond Ros, Nikolaus Hansen. A Simple Modification in CMA-ES Achieving Linear Time and Space Complexity. [Research Report] RR-6498, INRIA. 2008. ⟨inria-00270901v4⟩