We study the optimisation problem associated with Gaussian process regression using squared loss. The most common approach to this problem is to apply an exact solver, such as conjugate gradient descent, either directly on the problem or on a reduced-order version of it. However, stochastic gradient descent has recently gained traction in the Gaussian process literature, driven largely by its successes in deep learning. In this paper, we show that this approach when done right---by which we mean using specific insights from the optimisation and kernel communities---is highly effective.We thus introduce a particular stochastic dual gradient descent algorithm, conveniently implementable with a few lines of code using any deep learning framework. We explain our design decisions by illustrating their advantage against alternatives with ablation studies.We then show that the new method is highly competitive: our evaluations on standard regression benchmarks and a Bayesian optimisation task set our approach apart from conjugate gradients, variational Gaussian process approximations, and a prior version of stochastic gradient descent tailored for Gaussian processes. On a molecular binding affinity prediction task, our method places Gaussian process regression on par in terms of performance with graph neural networks.
Stochastic Gradient Descent for Gaussian Processes Done Right
Jihao Andreas Lin Shreyas Padhy Javier Antoran Austin Tripp Alexander Terenin Csaba Szepesvari José Miguel Hernández-Lobato David Janz