  With a principled representation of uncertainty and closed form posterior
updates, Gaussian processes (GPs) are a natural choice for online decision
making. However, Gaussian processes typically require at least
$\mathcal{O}(n^2)$ computations for $n$ training points, limiting their general
applicability. Stochastic variational Gaussian processes (SVGPs) can provide
scalable inference for a dataset of fixed size, but are difficult to
efficiently condition on new data. We propose online variational conditioning
(OVC), a procedure for efficiently conditioning SVGPs in an online setting that
does not require re-training through the evidence lower bound with the addition
of new data. OVC enables the pairing of SVGPs with advanced look-ahead
acquisition functions for black-box optimization, even with non-Gaussian
likelihoods. We show OVC provides compelling performance in a range of
applications including active learning of malaria incidence, and reinforcement
learning on MuJoCo simulated robotic control tasks.
