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Variance reduction for sequential sampling in stochastic programming

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Abstract

This paper investigates the variance reduction techniques Antithetic Variates (AV) and Latin Hypercube Sampling (LHS) when used for sequential sampling in stochastic programming and presents a comparative computational study. It shows conditions under which the sequential sampling with AV and LHS satisfy finite stopping guarantees and are asymptotically valid, discussing LHS in detail. It computationally compares their use in both the sequential and non-sequential settings through a collection of two-stage stochastic linear programs with different characteristics. The numerical results show that while both AV and LHS can be preferable to random sampling in either setting, LHS typically dominates in the non-sequential setting while performing well sequentially and AV gains some advantages in the sequential setting. These results imply that, given the ease of implementation of these variance reduction techniques, armed with the same theoretical properties and improved empirical performance relative to random sampling, AV and LHS sequential procedures present attractive alternatives in practice for a class of stochastic programs.

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Acknowledgements

The authors are grateful to Andrzej Ruszczyński and Artur Świetanowski for access to their regularized decomposition code, which was used to solve the test problems. The authors are also grateful to an anonymous referee whose insightful comments led to a significantly improved paper. Allocation of computer time from the Ohio Supercomputer Center (1987) is also gratefully acknowledged. This research has been partially funded by the National Science Foundation through grant CMMI-1345626 and the Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, Applied Mathematics program under Contract Number DE-AC02-06CH11357.

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  1. Department of Integrated Systems Engineering, The Ohio State University, Columbus, OH, 43210, USA

    Jangho Park & Güzin Bayraksan

  2. Birmingham, MI, USA

    Rebecca Stockbridge

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Correspondence to Güzin Bayraksan.

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Park, J., Stockbridge, R. & Bayraksan, G. Variance reduction for sequential sampling in stochastic programming. Ann Oper Res 300, 171–204 (2021). https://doi.org/10.1007/s10479-020-03908-x

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