## 1 Introduction
[PERSON] and [PERSON] [10] construct weights based on various ML models, such as kernel density estimation, \(k\)-nearest-neighbors (kNN) regression, and tree-based methods (i.e., classification and regression trees and random forest). [PERSON] and [PERSON] [10] demonstrate that the resulting wSAA problem can be solved in polynomial time given certain conditions (Theorem 2 in [PERSON] and [PERSON] [10]). They also demonstrate the asymptotic optimality of this framework--whether the data-driven decision converges to the full-information optimal solution as the data size grows to infinity. [PERSON] and [PERSON] [12] propose a kernel optimization method to solve the feature-based newsvendor problem, in which they assign weights to each historical sample by the Nadaraya-Watson estimator [17, 18]. They also show the generalization bounds--how well the performance of a prediction model, fitted on finite training data, generalizes out of sample [6, 19]. [PERSON] and [PERSON] [11] further learn effective forest-based CSO policies that integrate prediction and optimization, in which they also reweight each historical sample and solve the weighted sample analogue of the original CSO problem. For detailed reviews of corresponding prescriptive analytics frameworks for CSO problems, we refer to [PERSON] et al. [1] and [PERSON] and [PERSON] [6]. Secondly, our work contributes to the literature that explores the influence of data size on data-driven decisions. Much of this literature focuses solely on previous samples of uncertainty, not considering contextual covariates. Our main idea is closely aligned with a recent study by [PERSON] and [PERSON] [20], which presents a surprising finding: the worst-case relative regret of the SAA method is not monotonically related to the number of available samples, implying an influx of information could potentially harm decision quality. In contrast, our work examines the decision performance of the wSAA framework across a limited data size. To achieve this aim, we show two CSO problems with non-linear maximization objectives. We examine the minimum relative regret--the difference between the expected optimal profit of the oracle and the maximum expected out-of-sample profit incurred by the data-driven policy, normalized by the former profit--of the wSAA framework with limited data samples. Our analysis reveals the following intriguing finding:  
_The minimum relative regret of the wSAA framework can approach one with limited data samples._  
The value of one in this context indicates a total divergence between the expected profit from the oracle and the maximum expected profit obtained by the data-driven policy under the wSAA framework. That is to say, when the relative regret equals one, the data-driven policy under the wSAA framework performs as poorly as possible compared to the oracle. This interpretation underlines a considerable disparity between the decision-making efficacy of the wSAA framework and that of an oracle. Consequently, the primary contribution of our work lies in highlighting that the wSAA framework may not always effectively manage CSO problems when data samples are limited. We illustrate this observation through two straightforward examples, thus paving the way for future research to potentially attain optimal decision performance of the wSAA framework, contingent upon data size. The remainder of this paper is organized as follows. In Section 2, we introduce the wSAA framework mathematically. In Section 3, we present our findings through two CSO problems. Section 4 concludes and outlines future research directions.