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Distributionally robust SDDP

Author

Listed:
  • A. B. Philpott

    (The University of Auckland)

  • V. L. Matos

    (Plan4 Engenharia)

  • L. Kapelevich

    (The University of Auckland)

Abstract

We study a version of stochastic dual dynamic programming (SDDP) with a distributionally robust objective. The classical SDDP algorithm uses a finite (nominal) probability distribution for the random outcomes at each stage. We modify this by defining a distributional uncertainty set in each stage to be a Euclidean neighbourhood of the nominal probability distribution. We derive a formula for the worst-case expectation of future costs over this set that can be applied in the backward pass of SDDP. We verify the correctness of this algorithm, show its almost sure convergence under standard assumptions, and illustrate it by applying it to a model of the New Zealand hydrothermal electricity system.

Suggested Citation

  • A. B. Philpott & V. L. Matos & L. Kapelevich, 2018. "Distributionally robust SDDP," Computational Management Science, Springer, vol. 15(3), pages 431-454, October.
    • Handle: RePEc:spr:comgts:v:15:y:2018:i:3:d:10.1007_s10287-018-0314-0
    DOI: 10.1007/s10287-018-0314-0
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    References listed on IDEAS

    as
    1. Shapiro, Alexander, 2011. "Analysis of stochastic dual dynamic programming method," European Journal of Operational Research, Elsevier, vol. 209(1), pages 63-72, February.
    2. Andy Philpott & Vitor de Matos & Erlon Finardi, 2013. "On Solving Multistage Stochastic Programs with Coherent Risk Measures," Operations Research, INFORMS, vol. 61(4), pages 957-970, August.
    3. Philpott, A.B. & de Matos, V.L., 2012. "Dynamic sampling algorithms for multi-stage stochastic programs with risk aversion," European Journal of Operational Research, Elsevier, vol. 218(2), pages 470-483.
    4. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
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    Cited by:

    1. Oscar Dowson & Lea Kapelevich, 2021. "SDDP.jl : A Julia Package for Stochastic Dual Dynamic Programming," INFORMS Journal on Computing, INFORMS, vol. 33(1), pages 27-33, January.
    2. Bakker, Hannah & Dunke, Fabian & Nickel, Stefan, 2020. "A structuring review on multi-stage optimization under uncertainty: Aligning concepts from theory and practice," Omega, Elsevier, vol. 96(C).
    3. D. Ávila & A. Papavasiliou & N. Löhndorf, 2022. "Parallel and distributed computing for stochastic dual dynamic programming," Computational Management Science, Springer, vol. 19(2), pages 199-226, June.
    4. Park, Jangho & Bayraksan, Güzin, 2023. "A multistage distributionally robust optimization approach to water allocation under climate uncertainty," European Journal of Operational Research, Elsevier, vol. 306(2), pages 849-871.
    5. Thuener Silva & Davi Valladão & Tito Homem-de-Mello, 2021. "A data-driven approach for a class of stochastic dynamic optimization problems," Computational Optimization and Applications, Springer, vol. 80(3), pages 687-729, December.

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