# Calibration of Distributionally Robust Empirical Optimization Models

arXiv: https://arxiv.org/abs/1711.06565 · HTML: https://mlsanity.com/paper/1711.06565/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Nov 2017.

## Built on by (most cited first, 6 of 6)

- [Generalization Bounds with Minimal Dependency on Hypothesis Class via Distributionally Robust Optimization](https://mlsanity.com/paper/2106.11180/) (2021)
- [Learning and Decision-Making with Data: Optimal Formulations and Phase Transitions](https://mlsanity.com/paper/2109.06911/) (2021)
- [Decision Making under the Exponential Family: Distributionally Robust Optimisation with Bayesian Ambiguity Sets](https://mlsanity.com/paper/2411.16829/) (2024)
- [Distributional Robustness Bounds Generalization Errors](https://mlsanity.com/paper/2212.09962/) (2022)
- [Distributionally Robust Optimisation with Bayesian Ambiguity Sets](https://mlsanity.com/paper/2409.03492/) (2024)
- [An integrated perspective of robustness in regression through the lens of the bias-variance trade-off](https://mlsanity.com/paper/2407.10418/) (2024)

## Abstract (arXiv)

We study the out-of-sample properties of robust empirical optimization problems with smooth φ-divergence penalties and smooth concave objective functions, and develop a theory for data-driven calibration of the non-negative "robustness parameter" δ 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., δ 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.