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We introduce Kalman Gradient Descent, a stochastic optimization algorithmthat uses Kalman filtering to adaptively reduce gradient variance in stochasticgradient descent by filtering the gradient estimates. We present both atheoretical analysis of convergence in a non-convex setting and experimentalresults which demonstrate improved performance on a variety of machine learningareas including neural networks and black box variational inference. We alsopresent a distributed version of our algorithm that enables large-dimensionaloptimization, and we extend our algorithm to SGD with momentum and RMSProp.

Kalman Gradient Descent: Adaptive Variance Reduction in Stochastic Optimization