ICML 2019oral47 citations
Concentration Inequalities for Conditional Value at Risk
Philip Thomas, Erik Learned-Miller
Abstract
In this paper we derive new concentration inequalities for the conditional value at risk (CVaR) of a random variable, and compare them to the previous state of the art (Brown, 2007). We show analytically that our lower bound is strictly tighter than Brown’s, and empirically that this difference is significant. While our upper bound may be looser than Brown’s in some cases, we show empirically that in most cases our bound is significantly tighter. After discussing when each upper bound is superior, we conclude with empirical results which suggest that both of our bounds will often be significantly tighter than Brown’s.
BibTeX
@InProceedings{pmlr-v97-thomas19a,
title = {Concentration Inequalities for Conditional Value at Risk},
author = {Thomas, Philip and Learned-Miller, Erik},
booktitle = {Proceedings of the 36th International Conference on Machine Learning},
pages = {6225--6233},
year = {2019},
editor = {Chaudhuri, Kamalika and Salakhutdinov, Ruslan},
volume = {97},
series = {Proceedings of Machine Learning Research},
month = {09--15 Jun},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v97/thomas19a/thomas19a.pdf},
url = {https://proceedings.mlr.press/v97/thomas19a.html},
abstract = {In this paper we derive new concentration inequalities for the conditional value at risk (CVaR) of a random variable, and compare them to the previous state of the art (Brown, 2007). We show analytically that our lower bound is strictly tighter than Brown’s, and empirically that this difference is significant. While our upper bound may be looser than Brown’s in some cases, we show empirically that in most cases our bound is significantly tighter. After discussing when each upper bound is superior, we conclude with empirical results which suggest that both of our bounds will often be significantly tighter than Brown’s.}
}