Optimization with gradient-boosted trees and risk control

Abstract

Decision trees effectively represent the sparse, high dimensional and noisy nature of chemical data from experiments. Having learned a function from this data, we may want to thereafter optimize the function, e.g., picking the best chemical process catalyst. In this way, we may repurpose legacy predictive models. This work studies a large-scale, industrially-relevant mixed-integer quadratic optimization problem involving: (i) gradient-boosted pre-trained regression trees modeling catalyst behavior, (ii) penalty functions mitigating risk, and (iii) penalties enforcing composition constraints. We develop heuristic methods and an exact, branch-and-bound algorithm leveraging structural properties of gradient-boosted trees and penalty functions. We numerically test our methods on an industrial instance.