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Distributionally Robust Optimization (DRO) has been shown to provide a flexible framework for decision making under uncertainty and statistical estimation. For example, recent works in DRO have shown that popular statistical estimators can be interpreted as the solutions of suitable formulated data-driven DRO problems. In turn, this connection is used to optimally select tuning parameters in terms of a principled approach informed by robustness considerations. This paper contributes to this growing literature, connecting DRO and statistics, by showing how boosting algorithms can be studied via DRO. We propose a boosting type algorithm, named DRO-Boosting, as a procedure to solve our DRO formulation. Our DRO-Boosting algorithm recovers Adaptive Boosting (AdaBoost) in particular, thus showing that AdaBoost is effectively solving a DRO problem. We apply our algorithm to a financial dataset on credit card default payment prediction. Our approach compares favorably to alternative boosting methods which are widely used in practice.
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Statistical Limit Theorems in Distributionally Robust Optimization
The goal of this paper is to develop a methodology for the systematic analysis of asymptotic statistical properties of data-driven DRO formulations based on their corresponding non-DRO counterparts. We illustrate our approach in various settings, including both phidivergence and Wasserstein uncertainty sets. Different types of asymptotic behaviors are obtained depending on the rate at which the uncertainty radius decreases to zero as a function of the sample size and the geometry of the uncertainty sets.
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- PAR ID:
- 10483211
- Publisher / Repository:
- arxiv
- Date Published:
- Journal Name:
- arXivorg
- ISSN:
- 2331-8422
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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