A Deficiency of the Weighted Sample Average Approximation (wSAA) Framework: Unveiling the Gap between Data-Driven Policies and Oracles

Abstract

This paper critically examines the weighted sample average approximation (wSAA) framework, a widely used approach in prescriptive analytics for managing uncertain optimization problems featuring non-linear objectives. Our research pinpoints a key deficiency of the wSAA framework: when data samples are limited, the minimum relative regret—the discrepancy between the expected optimal profit realized by an oracle aware of the genuine distribution, and the maximum expected out-of-sample profit garnered by the data-driven policy, normalized by the former profit—can approach towards one. To validate this assertion, we scrutinize two distinct contextual stochastic optimization problems—the production decision-making problem and the ship maintenance optimization problem—within the wSAA framework. Our study exposes a potential deficiency of the wSAA framework: its decision performance markedly deviates from the full-information optimal solution under limited data samples. This finding offers valuable insights to both researchers and practitioners employing the wSAA framework.

A Deficiency of the Predict-Then-Optimize Framework: Decreased Decision Quality with Increased Data Size

“…Other studies concerning bounds on probabilistic guarantees of the relative regret of the SAA include Levi et al [22] and Cheung and Simchi-Levi [23]. Recently, Wang and Tian [24] investigate the decision performance of the wSAA framework across data sizes. In contrast, our work examines the decision performance of the PO framework across data sizes.…”