  We consider the problem of estimating a good maximizer of a black-box
function given noisy examples. To solve such problems, we propose to fit a new
type of function which we call a global optimization network (GON), defined as
any composition of an invertible function and a unimodal function, whose unique
global maximizer can be inferred in $\mathcal{O}(D)$ time. In this paper, we
show how to construct invertible and unimodal functions by using linear
inequality constraints on lattice models. We also extend to \emph{conditional}
GONs that find a global maximizer conditioned on specified inputs of other
dimensions. Experiments show the GON maximizers are statistically significantly
better predictions than those produced by convex fits, GPR, or DNNs, and are
more reasonable predictions for real-world problems.
