Large-Scale Gaussian Process Regression via Doubly Stochastic Gradient Descent

Gaussian process regression (GPR) is a popular tool for nonlinear function approximation. Unfortunately, GPR can be difficult to use in practice due to the O(n) memory and O(n) processing requirements for n training data points. We propose a novel approach to scaling up GPR to handle large datasets using the recent concept of doubly stochastic functional gradients. Our approach relies on the fact that GPR can be expressed as a convex optimization problem that can be solved by making two unbiased stochastic approximations to the functional gradient, one using random training points and another using random features, and then descending using this noisy functional gradient. The effectiveness of the resulting algorithm is evaluated on the wellknown problem of learning the inverse dynamics of a robot manipulator.