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Evolutionary Strategies (ES) are known to be an effective black-boxoptimization technique for deep neural networks when the true gradients cannotbe computed, such as in Reinforcement Learning. We continue a recent line ofresearch that uses surrogate gradients to improve the gradient estimation ofES. We propose a novel method to optimally incorporate surrogate gradientinformation. Our approach, unlike previous work, needs no information about thequality of the surrogate gradients and is always guaranteed to find a descentdirection that is better than the surrogate gradient. This allows toiteratively use the previous gradient estimate as surrogate gradient for thecurrent search point. We theoretically prove that this yields fast convergenceto the true gradient for linear functions and show under simplifyingassumptions that it significantly improves gradient estimates for generalfunctions. Finally, we evaluate our approach empirically on MNIST andreinforcement learning tasks and show that it considerably improves thegradient estimation of ES at no extra computational cost.

Improving Gradient Estimation in Evolutionary Strategies With Past Descent Directions