Statistical Properties of Robust Satisficing

TL;DR

This paper provides a comprehensive statistical analysis of the Robust Satisficing (RS) model, demonstrating its advantages over DRO and ERM in terms of simplicity, robustness, and practical performance under distribution shifts.

Contribution

It introduces the first statistical guarantees for RS, including confidence intervals and generalization bounds, and compares its robustness and hyperparameter sensitivity to DRO and ERM.

Findings

RS offers two-sided confidence intervals without minimax optimization.

RS outperforms ERM in small-sample and distribution shift scenarios.

RS shows lower hyperparameter sensitivity than DRO.

Abstract

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.