Calibration of Distributionally Robust Empirical Optimization Models
Michael Jong Kim and
Andrew E. B. Lim
Papers from arXiv.org
We study the out-of-sample properties of robust empirical optimization problems with smooth $\phi$-divergence penalties and smooth concave objective functions, and develop a theory for data-driven calibration of the non-negative "robustness parameter" $\delta$ that controls the size of the deviations from the nominal model. Building on the intuition that robust optimization reduces the sensitivity of the expected reward to errors in the model by controlling the spread of the reward distribution, we show that the first-order benefit of ``little bit of robustness" (i.e., $\delta$ small, positive) is a significant reduction in the variance of the out-of-sample reward while the corresponding impact on the mean is almost an order of magnitude smaller. One implication is that substantial variance (sensitivity) reduction is possible at little cost if the robustness parameter is properly calibrated. To this end, we introduce the notion of a robust mean-variance frontier to select the robustness parameter and show that it can be approximated using resampling methods like the bootstrap. Our examples show that robust solutions resulting from "open loop" calibration methods (e.g., selecting a $90\%$ confidence level regardless of the data and objective function) can be very conservative out-of-sample, while those corresponding to the robustness parameter that optimizes an estimate of the out-of-sample expected reward (e.g., via the bootstrap) with no regard for the variance are often insufficiently robust.
Date: 2017-11, Revised 2020-05
New Economics Papers: this item is included in nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1) Track citations by RSS feed
Downloads: (external link)
http://arxiv.org/pdf/1711.06565 Latest version (application/pdf)
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1711.06565
Access Statistics for this paper
More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().