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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. 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).
    3. 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.
    4. Johannes O. Royset & Roger J-B Wets, 2016. "Optimality Functions and Lopsided Convergence," Journal of Optimization Theory and Applications, Springer, vol. 169(3), pages 965-983, June.

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