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On sample size control in sample average approximations for solving smooth stochastic programs

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  • Johannes Royset

Abstract

We consider smooth stochastic programs and develop a discrete-time optimal-control problem for adaptively selecting sample sizes in a class of algorithms based on variable sample average approximations (VSAA). The control problem aims to minimize the expected computational cost to obtain a near-optimal solution of a stochastic program and is solved approximately using dynamic programming. The optimal-control problem depends on unknown parameters such as rate of convergence, computational cost per iteration, and sampling error. Hence, we implement the approach within a receding-horizon framework where parameters are estimated and the optimal-control problem is solved repeatedly during the calculations of a VSAA algorithm. The resulting sample-size selection policy consistently produces near-optimal solutions in short computing times as compared to other plausible policies in several numerical examples. Copyright Springer Science+Business Media New York (outside the USA) 2013

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  • Johannes Royset, 2013. "On sample size control in sample average approximations for solving smooth stochastic programs," Computational Optimization and Applications, Springer, vol. 55(2), pages 265-309, June.
    • Handle: RePEc:spr:coopap:v:55:y:2013:i:2:p:265-309
    DOI: 10.1007/s10589-012-9528-1
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    References listed on IDEAS

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    Cited by:

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    2. Yan, Pengyu & Yu, Kaize & Chao, Xiuli & Chen, Zhibin, 2023. "An online reinforcement learning approach to charging and order-dispatching optimization for an e-hailing electric vehicle fleet," European Journal of Operational Research, Elsevier, vol. 310(3), pages 1218-1233.
    3. Hu, Shaolong & Dong, Zhijie Sasha & Dai, Rui, 2024. "A machine learning based sample average approximation for supplier selection with option contract in humanitarian relief," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 186(C).
    4. Emelogu, Adindu & Chowdhury, Sudipta & Marufuzzaman, Mohammad & Bian, Linkan & Eksioglu, Burak, 2016. "An enhanced sample average approximation method for stochastic optimization," International Journal of Production Economics, Elsevier, vol. 182(C), pages 230-252.
    5. Hu, Shaolong & Hu, Qingmi & Tao, Sha & Dong, Zhijie Sasha, 2023. "A multi-stage stochastic programming approach for pre-positioning of relief supplies considering returns," Socio-Economic Planning Sciences, Elsevier, vol. 88(C).

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