Adaptive coordinate descent

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Abstract
Independence from the coordinate system is one source of efficiency and robustness for the Covariance Matrix Adaptation Evolution Strategy (CMA-ES). The recently proposed Adaptive Encoding (AE) procedure generalizes CMA-ES adaptive mechanism, and can be used together with any optimization algorithm. Adaptive Encoding gradually builds a transformation of the coordinate system such that the new coordinates are as decorrelated as possible with respect to the objective function. But any optimization algorithm can then be used together with Adaptive Encoding, and this paper proposes to use one of the simplest of all, that uses a dichotomy procedure on each coordinate in turn. The resulting algorithm, termed Adaptive Coordinate Descent (ACiD), is analyzed on the Sphere function, and experimentally validated on BBOB testbench where it is shown to outperform the standard (1+1)-CMA-ES, and is found comparable to other state-of-the-art CMA-ES variants.