Title: Improving Gradient Estimation in Evolutionary Strategies With Past Descent Directions. Abstract: We propose a novel method to optimally incorporate surrogate gradient information.  Our approach, unlike previous work, needs no information about the quality of the surrogate gradients and is always guaranteed to find a descent direction that is better than the surrogate gradient. This allows to iteratively use the  previous gradient estimate as surrogate gradient for the current search point. We theoretically prove that this yields fast convergence  to the true gradient for linear functions and show under simplifying assumptions that it significantly improves gradient estimates for general functions. Finally, we evaluate our approach empirically on MNIST and reinforcement learning tasks and show that it considerably improves  the gradient estimation of ES at no  extra computational cost.