Robust Bayesian Satisficing

TL;DR

This paper introduces RoBOS, a novel robust Bayesian satisficing algorithm for noisy black-box optimization under distributional shifts, providing guarantees on regret and demonstrating effectiveness across learning problems.

Contribution

The paper proposes RoBOS, a new algorithm that guarantees sublinear regret under distribution shifts in Bayesian optimization, with a novel regret notion called satisficing regret.

Findings

RoBOS guarantees sublinear lenient regret under certain assumptions.

RoBOS achieves sublinear robust satisficing regret independent of distribution shift.

Empirical results show RoBOS outperforms distributionally robust optimization methods.

Abstract

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.