Recovering Best Statistical Guarantees via the Empirical Divergence-Based Distributionally Robust Optimization
By Henry Lam. 2016
121 citations recorded by the source corpus.
We investigate the use of distributionally robust optimization (DRO) as a tractable tool to recover the asymptotic statistical guarantees provided by the Central Limit Theorem, for maintaining the feasibility of an expected value constraint under ambiguous probability distributions. We show that using empirically defined Burg-entropy divergence balls to construct the DRO can attain such guarantees. These balls, however, are not reasoned from the standard data-driven DRO framework since by themselves they can have low or even zero probability of covering the true distribution. Rather, their superior statistical performances are endowed by linking the resulting DRO with empirical likelihood and empirical processes. We show that the sizes of these balls can be optimally calibrated using chi-square process excursion. We conduct numerical experiments to support our theoretical findings.
Subfields: Finance, Management Science and Operations Research, Statistics and Probability
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Finance
- Yang Kang
- Karthyek Murthy
- John C. Duchi
- Hamed Rahimian
- Sanjay Mehrotra
- Hongseok Namkoong
- Jose H. Blanchet
In Management Science and Operations Research
- Hongseok Namkoong
- John C. Duchi
- Jose H. Blanchet
- Karthyek Murthy
- Yang Kang
- Aman Sinha
- Hamed Rahimian
- Sanjay Mehrotra
In Statistics and Probability
- John C. Duchi
- Hongseok Namkoong
- Jose H. Blanchet
- Karthyek Murthy
- Yang Kang
- Aman Sinha
- Hamed Rahimian
- Sanjay Mehrotra
Citations in the corpus
- Certifying Some Distributional Robustness with Principled Adversarial Training (2017, background): “For example, Ben-Tal et al. [5], Lam [39] and Namkoong and Duchi [48] use convex optimization approaches for f -divergence balls.”
- Distributionally Robust Optimization: A Review (2019, background): “Other iterative primal methods that have been proposed to solve a DRO model include Lam and Ghosh [177] for χ2-distance, and Ghosh et al. [115], Namkoong and Duchi [208], Ghosh and Lam [114] for general φ-divergences.”
- Robust Wasserstein profile inference and applications to machine learning (2016, methodology): “A profile function based approach towards calibrating the radius of uncertainty in the context of empirical likelihood based DRO can be found in [26, 14, 20, 25].”