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Conditional Value at Risk (CVaR) is a 'coherent risk measure' which generalizes expectation (reduced to a boundary parameter setting).
Widely used in mathematical finance, it is garnering increasing interest in machine learning 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.
Author Information
Zakaria Mhammedi (The Australian National University and Data61)
Benjamin Guedj (Inria & University College London)
Benjamin Guedj is a tenured research scientist at Inria since 2014, affiliated to the Lille - Nord Europe research centre in France. He is also affiliated with the mathematics department of the University of Lille. Since 2018, he is a Principal Research Fellow at the Centre for Artificial Intelligence and Department of Computer Science at University College London. He is also a visiting researcher at The Alan Turing Institute. Since 2020, he is the founder and scientific director of The Inria London Programme, a strategic partnership between Inria and UCL as part of a France-UK scientific initiative. He obtained his Ph.D. in mathematics in 2013 from UPMC (Université Pierre & Marie Curie, France) under the supervision of Gérard Biau and Éric Moulines. Prior to that, he was a research assistant at DTU Compute (Denmark). His main line of research is in statistical machine learning, both from theoretical and algorithmic perspectives. He is primarily interested in the design, analysis and implementation of statistical machine learning methods for high dimensional problems, mainly using the PAC-Bayesian theory.
Robert Williamson (ANU)
Related Events (a corresponding poster, oral, or spotlight)
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2020 Spotlight: PAC-Bayesian Bound for the Conditional Value at Risk »
Tue Dec 8th 04:00 -- 04:10 PM Room Orals & Spotlights: Learning Theory
More from the Same Authors
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2020 Poster: Learning the Linear Quadratic Regulator from Nonlinear Observations »
Zakaria Mhammedi · Dylan Foster · Max Simchowitz · Dipendra Misra · Wen Sun · Akshay Krishnamurthy · Alexander Rakhlin · John Langford -
2019 Poster: PAC-Bayes Un-Expected Bernstein Inequality »
Zakaria Mhammedi · Peter Grünwald · Benjamin Guedj -
2019 Poster: Dichotomize and Generalize: PAC-Bayesian Binary Activated Deep Neural Networks »
Gaël Letarte · Pascal Germain · Benjamin Guedj · Francois Laviolette -
2018 Poster: Constant Regret, Generalized Mixability, and Mirror Descent »
Zakaria Mhammedi · Robert Williamson -
2018 Spotlight: Constant Regret, Generalized Mixability, and Mirror Descent »
Zakaria Mhammedi · Robert Williamson -
2017 Workshop: (Almost) 50 shades of Bayesian Learning: PAC-Bayesian trends and insights »
Benjamin Guedj · Pascal Germain · Francis Bach