Concentration bounds for CVaR estimation: The cases of light-tailed and heavy-tailed distributions

Sanjay P. Bhat and Prashanth L. A, Improved Concentration Bounds for Conditional Value-at-Risk and Cumulative Prospect Theory using Wasserstein distance , arXiv e-prints (2019), arXiv:1902.10709

Original

1902

Earlier work this paper cites.

William R Thompson, On the likelihood that one unknown probability exceeds another in view of the evidence of two samples , Biometrika 25

1933

Earlier work this paper cites.

Philippe Artzner, Freddy Delbaen, Jean-Marc Eber, and David Heath, Coherent measures of risk , Mathematical finance 9

1999

Earlier work this paper cites.

David B Brown, Large deviations bounds for estimating conditional value-at-risk , Operations Research Letters 35

2007

Earlier work this paper cites.

Robert J Serfling, Approximation theorems of mathematical statistics , vol. 162, John Wiley & Sons, 2009

2009

Earlier work this paper cites.

J. Y. Audibert, S. Bubeck, and R. Munos, Best arm identification in multi-armed bandits , Conference on Learning Theory, 2010, pp. 41–53

2010

Earlier work this paper cites.

Lihua Sun and L Jeff Hong, Asymptotic representations for importance-sampling estimators of value-at-risk and conditional value-at-risk , Operations Research Letters 38

2010

Cited alongside, same era.

Ying Wang and Fuqing Gao, Deviation inequalities for an estimator of the conditional value-at-risk , Operations Research Letters 38

2010

Cited alongside, same era.

A. Sani, A. Lazaric, and R. Munos, Risk-aversion in multi-armed bandits , Advances in Neural Information Processing Systems, 2012, pp. 3275–3283

2012

Cited alongside, same era.

Sébastien Bubeck, Nicolo Cesa-Bianchi, and Gábor Lugosi, Bandits with heavy tail , IEEE Transactions on Information Theory 59

2013

Cited alongside, same era.

Nicolas Galichet, Michele Sebag, and Olivier Teytaud, Exploration vs exploitation vs safety: Risk-aware multi-armed bandits , Asian Conference on Machine Learning, 2013, pp. 245–260

Nicolas Fournier and Arnaud Guillin, On the rate of convergence in wasserstein distance of the empirical measure , Probability Theory and Related Fields 162

2015

Later among the works it cites.

Yahel David and Nahum Shimkin, Pure exploration for max-quantile bandits , Joint European Conference on Machine Learning and Knowledge Discovery in Databases, Springer, 2016, pp. 556–571

2016

Later among the works it cites.

Yahel David, Balázs Szörényi, Mohammad Ghavamzadeh, Shie Mannor, and Nahum Shimkin, Pac bandits with risk constraints , International Symposium on Artificial Intelligence and Mathematics, 2018

2018

Later among the works it cites.

R. K. Kolla, L. A. Prashanth, S. P. Bhat, and K. Jagannathan, Concentration bounds for empirical conditional value-at-risk: The unbounded case , ArXiv e-prints (2018)

2018

Later among the works it cites.