Mixed-Integer Convex Nonlinear Optimization with Gradient-Boosted Trees Embedded

Decision trees usefully represent sparse, high-dimensional, and noisy data. Having learned a function from these data, we may want to thereafter integrate the into larger decision-making problem, for example, picking best chemical process catalyst. We study large-scale, industrially relevant mixed-integer nonlinear nonconvex optimization problem involving both gradient-boosted penalty functions mitigating risk. This with convex terms broadly applies optimizing pretrained regression tree models. makers wish optimize discrete models repurpose legacy predictive or they model that accurately represents data set. develop several heuristic methods find feasible solutions an exact branch-and-bound algorithm leveraging structural properties of functions. computationally test our on concrete mixture design instance catalysis industrial instance.