We propose ResidualPlanner, a matrix mechanism for marginals with Gaussian noise that is both optimal and scalable.

Mirror descent [37] is becoming increasingly popular in a variety of settings in optimization and machine learning. One reason for its success is the fact that mirror descent can be adapted to fit the geometry ofthe optimization problem athand bychoosing asuitable strictly convexpotential function,theso-calledmirrormap.

In this analysis, we assume that evaluating the GP prior mean and kernel functions (and the corresponding derivatives) takesO(1)time. For each fantasy model, we need to compute the posterior mean and covariance matrix for the L points (x,w1:L), on which we draw the sample paths. This results in a total cost ofO(KML2)to generate all samples. The SAA approach trades a stochastic optimization problem with a deterministic approximation, which can be efficiently optimized. Suppose that we are interested in the optimization problemminxEω[h(x,ω)].