The Robust Satisficing (RS) model is an emerging approach to robust
optimization, offering streamlined procedures and robust generalization across
various applications. However, the statistical theory of RS remains unexplored
in the literature. This paper fills in the gap by comprehensively analyzing the
theoretical properties of the RS model. Notably, the RS structure offers a more
straightforward path to deriving statistical guarantees compared to the seminal
Distributionally Robust Optimization (DRO), resulting in a richer set of
results. In particular, we establish two-sided confidence intervals for the
optimal loss without the need to solve a minimax optimization problem
explicitly. We further provide finite-sample generalization error bounds for
the RS optimizer. Importantly, our results extend to scenarios involving
distribution shifts, where discrepancies exist between the sampling and target
distributions. Our numerical experiments show that the RS model consistently
outperforms the baseline empirical risk minimization in small-sample regimes
and under distribution shifts. Furthermore, compared to the DRO model, the RS
model exhibits lower sensitivity to hyperparameter tuning, highlighting its
practicability for robustness considerations.

该研究论文综合分析了 Robust Satisficing（RS）模型的理论性质，包括在不同应用中提供简化程序和鲁棒性广义化。通过与 Distributionally Robust Optimization（DRO）进行比较，RS 模型的理论性质更容易获得统计保证，同时还提供了两侧的置信区间和有限样本广义化误差界。该模型在小样本环境和分布转移情景下相对于基准经验风险最小化表现更好，并且比 DRO 模型对超参数调整更不敏感，突显了它在鲁棒性考虑中的实用性。

鲁棒满足性的统计特性

Statistical Properties of Robust Satisficing

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.

分布变化、鲁棒满意度、上下文贝叶斯优化、RoBOS 和嘈杂黑盒优化是该研究论文的主要关键词和研究领域。