Assessing solution quality in risk-averse stochastic programs
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913815337107456 |
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| author | van Beesten, E. Ruben Koning, Nick W. Morton, David P. |
| author_facet | van Beesten, E. Ruben Koning, Nick W. Morton, David P. |
| contents | In optimization problems, 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 for risk-averse problems, standard estimators are optimistically biased, 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 optimality gap estimation methods from the risk-neutral case to the risk-averse case, such as the multiple replications procedure and its one- and two-sample variants. We show that our approach is tractable and leads to high-quality optimality gap estimates for spectral and quadrangle risk measures. Our approach can further make use of existing bias and variance reduction techniques. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_15690 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Assessing solution quality in risk-averse stochastic programs van Beesten, E. Ruben Koning, Nick W. Morton, David P. Optimization and Control Risk Management 90C15, 91B05 In optimization problems, 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 for risk-averse problems, standard estimators are optimistically biased, 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 optimality gap estimation methods from the risk-neutral case to the risk-averse case, such as the multiple replications procedure and its one- and two-sample variants. We show that our approach is tractable and leads to high-quality optimality gap estimates for spectral and quadrangle risk measures. Our approach can further make use of existing bias and variance reduction techniques. |
| title | Assessing solution quality in risk-averse stochastic programs |
| topic | Optimization and Control Risk Management 90C15, 91B05 |
| url | https://arxiv.org/abs/2408.15690 |