  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.
