Optimization problems with uncertain black-box constraints, modeled by warped Gaussian processes, have recently been considered in the Bayesian optimization setting. This presentation considers optimization problems with aggregated black-box constraints. Each aggregated black-box constraint sums several draws from the same black-box function with different decision variables as arguments in each individual black-box term. 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. Our approach considers uncertain functions modeled by warped Gaussian processes. We analyze convexity conditions and propose a custom global optimization strategy for non-convex cases. An industrially-relevant example from geothermal drilling illustrates that the approach effectively mitigates uncertainty in the learned curves.
Mar 25, 2022, 11:00 am – 12:00 pm