Robust sample average approximation
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10107_2017_1174_ReferencePDF.pdf
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Author(s)
Gupta, Vishal
Kallus, Nathan
Bertsimas, Dimitris J
Date Issued
June 2017
Journal
Mathematical Programming
Publisher
Springer Berlin Heidelberg
Citation
Bertsimas, Dimitris, et al. “Robust Sample Average Approximation.” Mathematical Programming, vol. 171, no. 1–2, Sept. 2018, pp. 217–82.
Version
Author's final manuscript
Abstract
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. Keywords: Sample average approximation of stochastic optimization, Data-driven optimization, Goodnessof-fit
testing, Distributionally robust optimization, Conic programming, Inventory management, Portfolio allocation
MIT Department
Sloan School of Management
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1007/s10107-017-1174-z
