Global Optimization Networks
This addresses the challenge of global optimization in noisy black-box settings, offering a more efficient and accurate method for real-world applications.
The paper tackles the problem of estimating maximizers of black-box functions from noisy data by proposing Global Optimization Networks (GONs), which combine invertible and unimodal functions to enable efficient global maximizer inference in O(D) time. Experiments show GONs produce statistically significantly better predictions than convex fits, GPR, or DNNs.
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.