Provably near-optimal approximation schemes for implicit stochastic and sample-based dynamic programs

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4 Scopus citations


In this paper, we address two models of nondeterministic discrete time finite-horizon dynamic programs (DPs): implicit stochastic DPs (the information about the random events is given by value oracles to their cumulative distribution functions) and sample-based DPs (the information about the random events is deduced by drawing random samples). Such data-driven models frequently appear in practice, where the cumulative distribution functions of the underlying random variables are either unavailable or too complicated to work with. In both models, the single-period cost functions are accessed via value oracle calls and assumed to possess either monotone or convex structure. We develop the first near-optimal relative approximation schemes for each of the two models. Applications in stochastic inventory control (that is, several variants of the so-called newsvendor problem) are discussed in detail. Our results are achieved by a combination of Bellman equation calculations, density estimation results, and extensions of the technique of K-approximation sets and functions introduced by Halman et al. (2009) [Halman N, Klabjan D, Mostagir M, Orlin J, Simchi-Levi D (2009) A fully polynomial time approximation scheme for single-item stochastic inventory control with discrete demand. Math. Oper. Res. 34(3):674–685.].

Original languageEnglish
Pages (from-to)1157-1181
Number of pages25
JournalINFORMS Journal on Computing
Issue number4
StatePublished - Sep 2020
Externally publishedYes

Bibliographical note

Publisher Copyright:
Copyright: © 2020 INFORMS


History: Accepted by Antonio Frangioni, Area Editor for Design & Analysis of Algorithms—Continuous and Karen Aardal, former Area Editor. Funding: The author was partially supported by the Israel Science Foundation [Grant 399/17] and the United States–Israel Binational Science Foundation [Grant 2018095]. Supplemental Material: The online appendix is available at

FundersFunder number
United States-Israel Binational Science Foundation2018095
Israel Science Foundation399/17


    • Approximation algorithms
    • Inventory control
    • K-approximation sets and functions
    • Sample average approximation


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