Online evolution strategies have become an attractive alternative to automatic differentiation (AD) due to their ability to handle chaotic and black-box loss functions, while also allowing more frequent gradient updates than vanilla Evolution Strategies (ES). In this work, we propose a general class of unbiased online evolution strategies. We analytically and empirically characterize the variance of this class of gradient estimators and identify the one with the least variance, which we term Noise-Reuse Evolution Strategies (NRES). Experimentally, we show that NRES results in faster convergence than existing AD and ES methods in terms of wall-clock speed and total number of unroll steps across a variety of applications, including learning dynamical systems, meta-training learned optimizers, and reinforcement learning.

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