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PAC-Bayesian Bound for the Conditional Value at Risk

Zakaria Mhammedi 1 Benjamin Guedj 2, 3, 4, 5 Robert C. Williamson
5 MODAL - MOdel for Data Analysis and Learning
LPP - Laboratoire Paul Painlevé - UMR 8524, Université de Lille, Sciences et Technologies, Inria Lille - Nord Europe, CERIM - Santé publique : épidémiologie et qualité des soins-EA 2694, Polytech Lille - École polytechnique universitaire de Lille
Abstract : Conditional Value at Risk (CVAR) is a family of "coherent risk measures" which generalize the traditional mathematical expectation. Widely used in mathematical finance, it is garnering increasing interest in machine learning, e.g., as an alternate approach to regularization, and as a means for ensuring fairness. This paper presents a generalization bound for learning algorithms that minimize the CVAR of the empirical loss. The bound is of PAC-Bayesian type and is guaranteed to be small when the empirical CVAR is small. We achieve this by reducing the problem of estimating CVAR to that of merely estimating an expectation. This then enables us, as a by-product, to obtain concentration inequalities for CVAR even when the random variable in question is unbounded.
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https://hal.inria.fr/hal-02883728
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Submitted on : Monday, June 29, 2020 - 12:58:04 PM
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  • HAL Id : hal-02883728, version 1
  • ARXIV : 2006.14763

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Zakaria Mhammedi, Benjamin Guedj, Robert C. Williamson. PAC-Bayesian Bound for the Conditional Value at Risk. 2020. ⟨hal-02883728⟩

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