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Assessing solution quality in risk-averse stochastic programs

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  • E. Ruben van Beesten
  • Nick W. Koning
  • David P. Morton

Abstract

In an optimization problem, the quality of a candidate solution can be characterized by the optimality gap. For most stochastic optimization problems, this gap must be statistically estimated. We show that standard estimators are optimistically biased for risk-averse problems, which compromises the statistical guarantee on the optimality gap. We introduce estimators for risk-averse problems that do not suffer from this bias. Our method relies on using two independent samples, each estimating a different component of the optimality gap. Our approach extends a broad class of methods for estimating the optimality gap from the risk-neutral case to the risk-averse case, such as the multiple replications procedure and its one- and two-sample variants. Our approach can further make use of existing bias and variance reduction techniques.

Suggested Citation

  • E. Ruben van Beesten & Nick W. Koning & David P. Morton, 2024. "Assessing solution quality in risk-averse stochastic programs," Papers 2408.15690, arXiv.org.
    • Handle: RePEc:arx:papers:2408.15690
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    References listed on IDEAS

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    1. Rebecca Stockbridge & Güzin Bayraksan, 2016. "Variance reduction in Monte Carlo sampling-based optimality gap estimators for two-stage stochastic linear programming," Computational Optimization and Applications, Springer, vol. 64(2), pages 407-431, June.
    2. Jeff Linderoth & Alexander Shapiro & Stephen Wright, 2006. "The empirical behavior of sampling methods for stochastic programming," Annals of Operations Research, Springer, vol. 142(1), pages 215-241, February.
    3. Vitor L. de Matos & David P. Morton & Erlon C. Finardi, 2017. "Assessing policy quality in a multistage stochastic program for long-term hydrothermal scheduling," Annals of Operations Research, Springer, vol. 253(2), pages 713-731, June.
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