Distributional shifts pose a significant challenge to achieving robustness in contemporary machine learning. To overcome this challenge, robust satisficing (RS) seeks a robust solution to an unspecified distributional shift while achieving a utility above a desired threshold. This paper focuses on the problem of RS in contextual Bayesian optimization when there is a discrepancy between the true and reference distributions of the context. We propose a novel robust Bayesian satisficing algorithm called RoBOS for noisy black-box optimization. Our algorithm guarantees sublinear lenient regret under certain assumptions on the amount of distribution shift. In addition, we define a weaker notion of regret called robust satisficing regret, in which our algorithm achieves a sublinear upper bound independent of the amount of distribution shift. To demonstrate the effectiveness of our method, we apply it to various learning problems and compare it to other approaches, such as distributionally robust optimization.

翻译：分布偏移对当代机器学习实现鲁棒性构成了重大挑战。为应对这一挑战，鲁棒满足（RS）方法旨在寻找一种针对未指定分布偏移的鲁棒解，同时确保效用超过期望阈值。本文聚焦于当上下文真实分布与参考分布存在差异时，上下文贝叶斯优化中的鲁棒满足问题。我们提出了一种新颖的鲁棒贝叶斯满足算法RoBOS，用于处理含噪声的黑箱优化问题。该算法在满足分布偏移量的特定假设条件下，能够保证亚线性的宽松遗憾。此外，我们定义了一种称为鲁棒满足遗憾的较弱遗憾概念，在此概念下，我们的算法可达到与分布偏移量无关的亚线性上界。为验证所提方法的有效性，我们将其应用于多种学习问题，并与分布鲁棒优化等其他方法进行了对比。