A robust approach to warped Gaussian process-constrained optimization

• 成果类型: Article
• 署名作者: Wiebe, J.; Cecilio, I; Dunlop, J.; Misener, R.
• 署名单位: Imperial College London; Schlumberger
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-021-01762-8
• 发表日期: 2022
• 页码: 805-839
• 关键词: global optimization; Bayesian optimization; continuous-time; approximation; algorithm; PROGRAMS; OIL

摘要

Optimization problems with uncertain black-box constraints, modeled by warped Gaussian processes, have recently been considered in the Bayesian optimization setting. This work 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. While robust optimization typically considers parametric uncertainty, 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. 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.