# Robust Sample Average Approximation

arXiv: https://arxiv.org/abs/1408.4445 · HTML: https://mlsanity.com/paper/1408.4445/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Aug 2014.

## Built on by (most cited first, 25 of 25)

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- [Estimate-Then-Optimize versus Integrated-Estimation-Optimization versus Sample Average Approximation: A Stochastic Dominance Perspective](https://mlsanity.com/paper/2304.06833/) (2023)
- [Holistic Robust Data-Driven Decisions](https://mlsanity.com/paper/2207.09560/) (2022)
- [Treatment Effect Risk: Bounds and Inference](https://mlsanity.com/paper/2201.05893/) (2022)
- [Efficient Algorithms for Empirical Group Distributionally Robust Optimization and Beyond](https://mlsanity.com/paper/2403.03562/) (2024)
- [Generalization Bounds with Minimal Dependency on Hypothesis Class via Distributionally Robust Optimization](https://mlsanity.com/paper/2106.11180/) (2021)
- [Beyond IID: data-driven decision-making in heterogeneous environments](https://mlsanity.com/paper/2206.09642/) (2022)
- [Learning and Decision-Making with Data: Optimal Formulations and Phase Transitions](https://mlsanity.com/paper/2109.06911/) (2021)
- [Smoothed f-Divergence Distributionally Robust Optimization](https://mlsanity.com/paper/2306.14041/) (2023)
- [Distributionally Robust Prescriptive Analytics with Wasserstein Distance](https://mlsanity.com/paper/2106.05724/) (2021)
- [Efficient Stochastic Approximation of Minimax Excess Risk Optimization](https://mlsanity.com/paper/2306.00026/) (2023)
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- [Conformalized Decision Risk Assessment](https://mlsanity.com/paper/2505.13243/) (2025)
- [PASTA: A Unified Framework for Offline Assortment Learning](https://mlsanity.com/paper/2510.01693/) (2025)
- [Calibrating Over-Parametrized Simulation Models: A Framework via Eligibility Set](https://mlsanity.com/paper/2105.12893/) (2021)
- [Semi-Variance Reduction for Fair Federated Learning](https://mlsanity.com/paper/2406.16193/) (2024)
- [FedMABA: Towards Fair Federated Learning through Multi-Armed Bandits Allocation](https://mlsanity.com/paper/2410.20141/) (2024)
- [Online Robust Planning under Model Uncertainty: A Sample-Based Approach](https://mlsanity.com/paper/2509.10162/) (2025)
- [On a class of data-driven mixed-integer programming problems under uncertainty: a distributionally robust approach](https://mlsanity.com/paper/2105.14139/) (2021)
- [Neural-Progressive Hedging: Enforcing Constraints in Reinforcement Learning with Stochastic Programming](https://mlsanity.com/paper/2202.13436/) (2022)
- [An Optimistic-Robust Approach for Dynamic Positioning of Omnichannel Inventories](https://mlsanity.com/paper/2310.12183/) (2023)
- [Mirror Descent Linearized Augmented Lagrangian Methods for Nonconvex Constrained Stochastic Zeroth-Order Optimization](https://mlsanity.com/paper/2504.09409/) (2025)
- [Prescribe-then-Select: Adaptive Policy Selection for Contextual Stochastic Optimization](https://mlsanity.com/paper/2509.08194/) (2025)

## Abstract (arXiv)

Sample average approximation (SAA) is a widely popular approach to data-driven decision-making under uncertainty. Under mild assumptions, SAA is both tractable and enjoys strong asymptotic performance guarantees. Similar guarantees, however, do not typically hold in finite samples. In this paper, we propose a modification of SAA, which we term Robust SAA, which retains SAA's tractability and asymptotic properties and, additionally, enjoys strong finite-sample performance guarantees. The key to our method is linking SAA, distributionally robust optimization, and hypothesis testing of goodness-of-fit. Beyond Robust SAA, this connection provides a unified perspective enabling us to characterize the finite sample and asymptotic guarantees of various other data-driven procedures that are based upon distributionally robust optimization. This analysis provides insight into the practical performance of these various methods in real applications. We present examples from inventory management and portfolio allocation, and demonstrate numerically that our approach outperforms other data-driven approaches in these applications.