A robust approach to warped Gaussian process-constrained optimization

TL;DR

This paper presents a robust optimization method for warped Gaussian process-constrained problems, transforming uncertain probabilistic constraints into deterministic ones, with applications in safety-critical and industrial scenarios.

Contribution

It introduces a novel approach extending robust optimization to uncertain functions modeled by warped Gaussian processes, including convexity analysis and a global optimization strategy for non-convex cases.

Findings

Effective mitigation of uncertainty in production planning and oil well drilling.

Successful application of the method to safety-critical and industrial problems.

Development of a custom global optimization strategy for integer decisions.

Abstract

Optimization problems with uncertain black-box constraints, modeled by warped Gaussian processes, have recently been considered in the Bayesian optimization setting. This work introduces a new class of constraints in which the same black-box function occurs multiple times evaluated at different domain points. Such constraints are important in applications where, e.g., safety-critical measures are aggregated over multiple time periods. Our approach, which uses robust optimization, reformulates these uncertain constraints into deterministic constraints guaranteed to be satisfied with a specified probability, i.e., deterministic approximations to a chance constraint. This approach extends robust optimization methods from parametric uncertainty to uncertain functions modeled by warped Gaussian processes. We analyze convexity conditions and propose a custom global optimization strategy for non-convex cases. A case study derived from production planning and an industrially relevant example from oil well drilling show that the approach effectively mitigates uncertainty in the learned curves. For the drill scheduling example, we develop a custom strategy for globally optimizing integer decisions.