一种鲁棒的变形高斯过程约束optimization算法
A robust approach to warped Gaussian process-constrained optimization
摘要：
具有不确定黑箱约束的最优化问题，由变形高斯过程建模，最近被认为是在贝叶斯优化设置。这项工作引入了一类新的约束，其中相同的黑盒函数在不同的域点处多次出现并进行评估。这样的约束在应用中是重要的，例如，安全关键措施在多个时间段上被聚合。我们的方法，它使用鲁棒优化，重新制定这些不确定的约束到确定性的约束，保证满足一个指定的概率，即，对机会约束的确定性近似。该方法将鲁棒最优化方法从参数不确定性扩展到由扭曲高斯过程建模的不确定函数。我们分析了凸性条件，并提出了一个自定义的全局优化策略的非凸情况。一个来自生产计划的案例研究和一个工业相关的例子，从油井钻井表明，该方法有效地减轻了学习曲线的不确定性。对于钻井调度的例子，我们开发了一个自定义的策略，全局优化整数决策。
英文摘要：
Optimization problems with uncertain black-box constraints, modeled by warped Gaussian processes, have recently been considered in the Bayesian optimization setting. This work 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.
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