Concentration Inequalities for Conditional Value at Risk

Philip Thomas, Erik Learned-Miller
Proceedings of the 36th International Conference on Machine Learning, PMLR 97:6225-6233, 2019.

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.

Cite this Paper

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.} }
Endnote
%0 Conference Paper %T Concentration Inequalities for Conditional Value at Risk %A Philip Thomas %A Erik Learned-Miller %B Proceedings of the 36th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2019 %E Kamalika Chaudhuri %E Ruslan Salakhutdinov %F pmlr-v97-thomas19a %I PMLR %P 6225--6233 %U https://proceedings.mlr.press/v97/thomas19a.html %V 97 %X 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.
APA
Thomas, P. & Learned-Miller, E.. (2019). Concentration Inequalities for Conditional Value at Risk. Proceedings of the 36th International Conference on Machine Learning, in Proceedings of Machine Learning Research 97:6225-6233 Available from https://proceedings.mlr.press/v97/thomas19a.html.

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