  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.
