Superquantiles at Work: Machine Learning Applications and Efficient Subgradient Computation

R. Tyrell Rockafellar and his collaborators introduced, in a series of works, new regression modeling methods based on the notion of superquantile (or conditional value-at-risk). These methods have been influential in economics, finance, management science, and operations research in general. Recent...

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Vydáno v:Set-valued and variational analysis Ročník 29; číslo 4; s. 967 - 996
Hlavní autoři: Laguel, Yassine, Pillutla, Krishna, Malick, Jérôme, Harchaoui, Zaid
Médium: Journal Article
Jazyk:angličtina
Vydáno: Dordrecht Springer Netherlands 01.12.2021
Springer Nature B.V
Springer
Témata:
Algorithms
Analysis
Convex and Variational Analysis
Machine learning
Mathematics
Mathematics and Statistics
Operations research
Optimization
Optimization and Control
Robustness (mathematics)
SI: Optimization
Robust optimization
Superquantiles
Smoothing
Machine learning
ISSN:1877-0533, 1877-0541
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Shrnutí:R. Tyrell Rockafellar and his collaborators introduced, in a series of works, new regression modeling methods based on the notion of superquantile (or conditional value-at-risk). These methods have been influential in economics, finance, management science, and operations research in general. Recently, they have been subject of a renewed interest in machine learning, to address issues of distributional robustness and fair allocation. In this paper, we review some of these new applications of the superquantile, with references to recent developments. These applications involve nonsmooth superquantile-based objective functions that admit explicit subgradient calculations. To make these superquantile-based functions amenable to the gradient-based algorithms popular in machine learning, we show how to smooth them by infimal convolution and detail numerical procedures to compute the gradients of the smooth approximations. We put the approach into perspective by comparing it to other smoothing techniques and by illustrating it on toy examples.
Bibliografie:ObjectType-Article-1
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ISSN:1877-0533
1877-0541
DOI:10.1007/s11228-021-00609-w