Robust Bayesian Satisficing
Artun Saday Yaşar Cahit Yıldırım Cem Tekin
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.