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Recently it was shown by Nesterov (2011) that techniques form convexoptimization can be used to successfully accelerate simple derivative-freerandomized optimization methods. The appeal of those schemes lies in their lowcomplexity, which is only $\Theta(n)$ per iteration---compared to $\Theta(n^2)$for algorithms storing second-order information or covariance matrices. From ahigh-level point of view, those accelerated schemes employ correlations betweensuccessive iterates---a concept looking similar to the evolution path used inCovariance Matrix Adaptation Evolution Strategies (CMA-ES).  In this contribution, we (i) implement and empirically test a simpleaccelerated random search scheme (SARP). Our study is the first to providenumerical evidence that SARP can effectively be implemented with adaptive stepsize control and does not require access to gradient or advanced line searchoracles. We (ii) try to empirically verify the supposed analogy between theevolution path and SARP. We propose an algorithm CMA-EP that uses only theevolution path to bias the search. This algorithm can be generalized to afamily of low memory schemes, with complexity $\Theta(mn)$ per iteration,following a recent approach by Loshchilov (2014). The study shows that theperformance of CMA-EP heavily depends on the spectra of the objective functionand thus it cannot accelerate as consistently as SARP.

On low complexity Acceleration Techniques for Randomized Optimization: Supplementary Online Material