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We introduce an acceleration for covariance matrix adaptation evolutionstrategies (CMA-ES) by means of adaptive diagonal decoding (dd-CMA). Thisdiagonal acceleration endows the default CMA-ES with the advantages ofseparable CMA-ES without inheriting its drawbacks. Technically, we introduce adiagonal matrix D that expresses coordinate-wise variances of the samplingdistribution in DCD form. The diagonal matrix can learn a rescaling of theproblem in the coordinates within linear number of function evaluations.Diagonal decoding can also exploit separability of the problem, but, crucially,does not compromise the performance on non-separable problems. The latter isaccomplished by modulating the learning rate for the diagonal matrix based onthe condition number of the underlying correlation matrix. dd-CMA-ES not onlycombines the advantages of default and separable CMA-ES, but may achieveoveradditive speedup: it improves the performance, and even the scaling, of thebetter of default and separable CMA-ES on classes of non-separable testfunctions that reflect, arguably, a landscape feature commonly observed inpractice.  The paper makes two further secondary contributions: we introduce twodifferent approaches to guarantee positive definiteness of the covariancematrix with active CMA, which is valuable in particular with large populationsize; we revise the default parameter setting in CMA-ES, proposing acceleratedsettings in particular for large dimension.  All our contributions can be viewed as independent improvements of CMA-ES,yet they are also complementary and can be seamlessly combined. In numericalexperiments with dd-CMA-ES up to dimension 5120, we observe remarkableimprovements over the original covariance matrix adaptation on functions withcoordinate-wise ill-conditioning. The improvement is observed also for largepopulation sizes up to about dimension squared.

Diagonal Acceleration for Covariance Matrix Adaptation Evolution Strategies