Distributionally robust optimization (DRO) is a powerful tool for decision making under uncertainty. It is particularly appealing because of its ability to leverage existing data. However, many practical problems call for decision- making with some auxiliary information, and DRO in the context of conditional distributions is not straightforward. We propose a conditional kernel distributionally robust optimiza- tion (CKDRO) method that enables robust decision making under conditional distributions through kernel DRO and the conditional mean operator in the reproducing kernel Hilbert space (RKHS). In particular, we consider problems where there is a correlation between the unknown variable y and an auxiliary observable variable x. Given past data of the two variables and a queried auxiliary variable, CKDRO represents the conditional distribution P(y|x) as the conditional mean operator in the RKHS space and quantifies the ambiguity set in the RKHS as well, which depends on the size of the dataset as well as the query point. To justify the use of RKHS, we demonstrate that the ambiguity set defined in RKHS can be viewed as a ball under a metric that is similar to the Wasserstein metric. The DRO is then dualized and solved via a finite dimensional convex program. The proposed CKDRO approach is applied to a generation scheduling problem and shows that the result of CKDRO is superior to common benchmarks in terms of quality and robustness.
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Distributionally robust learning-to-rank under the Wasserstein metric
Despite their satisfactory performance, most existing listwise Learning-To-Rank (LTR) models do not consider the crucial issue of robustness. A data set can be contaminated in various ways, including human error in labeling or annotation, distributional data shift, and malicious adversaries who wish to degrade the algorithm’s performance. It has been shown that Distributionally Robust Optimization (DRO) is resilient against various types of noise and perturbations. To fill this gap, we introduce a new listwise LTR model called Distributionally Robust Multi-output Regression Ranking (DRMRR) . Different from existing methods, the scoring function of DRMRR was designed as a multivariate mapping from a feature vector to a vector of deviation scores, which captures local context information and cross-document interactions. In this way, we are able to incorporate the LTR metrics into our model. DRMRR uses a Wasserstein DRO framework to minimize a multi-output loss function under the most adverse distributions in the neighborhood of the empirical data distribution defined by a Wasserstein ball. We present a compact and computationally solvable reformulation of the min-max formulation of DRMRR. Our experiments were conducted on two real-world applications: medical document retrieval and drug response prediction, showing that DRMRR notably outperforms state-of-the-art LTR models. We also conducted an extensive analysis to examine the resilience of DRMRR against various types of noise: Gaussian noise, adversarial perturbations, and label poisoning. Accordingly, DRMRR is not only able to achieve significantly better performance than other baselines, but it can maintain a relatively stable performance as more noise is added to the data.
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- NSF-PAR ID:
- 10424873
- Editor(s):
- Srinivasan, Kathiravan
- Date Published:
- Journal Name:
- PLOS ONE
- Volume:
- 18
- Issue:
- 3
- ISSN:
- 1932-6203
- Page Range / eLocation ID:
- e0283574
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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https://youtu.be/79Py8KU4_k0 (Ed.)We consider statistical methods that invoke a min-max distributionally robust formulation to extract good out-of-sample performance in data-driven optimization and learning problems. Acknowledging the distributional uncertainty in learning from limited samples, the min-max formulations introduce an adversarial inner player to explore unseen covariate data. The resulting distributionally robust optimization (DRO) formulations, which include Wasserstein DRO formulations (our main focus), are specified using optimal transportation phenomena. Upon describing how these infinite-dimensional min-max problems can be approached via a finite-dimensional dual reformulation, this tutorial moves into its main component, namely, explaining a generic recipe for optimally selecting the size of the adversary’s budget. This is achieved by studying the limit behavior of an optimal transport projection formulation arising from an inquiry on the smallest confidence region that includes the unknown population risk minimizer. Incidentally, this systematic prescription coincides with those in specific examples in high-dimensional statistics and results in error bounds that are free from the curse of dimensions. Equipped with this prescription, we present a central limit theorem for the DRO estimator and provide a recipe for constructing compatible confidence regions that are useful for uncertainty quantification. The rest of the tutorial is devoted to insights into the nature of the optimizers selected by the min-max formulations and additional applications of optimal transport projections.more » « less
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1371/journal.pone.0283574
