Qualitative and Quantitative Assessment of Step Size Adaptation Rules
Oswin Krause, Tobias Glasmachers, Christian Igel · 2017
We present a comparison of step size adaptation methods for evolution strategies, covering recent developments in the field. Following recent work by Hansen et al. we formulate a concise list of performance criteria: a) fast convergence of the mean, b) near-optimal fixed point of the normalized step size dynamics, and c) invariance to adding constant dimensions of the objective function. Our results show that algorithms violating these principles tend to underestimate the step size or are unreliable when the function does not fit to the algorithm's tuned hyperparameters. In contrast, we find that cumulative step size adaptation (CSA) and two-point adaptation (TPA) provide reliable estimates of the optimal step size. We further find that removing the evolution path of CSA still leads to a reliable algorithm without the computational requirements of CSA.