An exponential tail bound for lq stable learning rules, Aurélien Garivier and Satyen Kale, vol.98, pp.31-63, 2019. ,
Entropic value-at-risk: A new coherent risk measure, Journal of Optimization Theory and Applications, vol.155, issue.3, pp.1105-1123, 2012. ,
Le comportement de l'homme rationnel devant le risque: critique des postulats et axiomes de l'école américaine, Econometrica: Journal of the Econometric Society, pp.503-546, 1953. ,
Coherent measures of risk, Mathematical finance, vol.9, issue.3, pp.203-228, 1999. ,
Mirror descent and nonlinear projected subgradient methods for convex optimization, Operations Research Letters, vol.31, issue.3, pp.167-175, 2003. ,
Concentration of risk measures: A Wasserstein distance approach, Advances in Neural Information Processing Systems, pp.11739-11748, 2019. ,
Concentration inequalities, Summer School on Machine Learning, pp.208-240, 2003. ,
URL : https://hal.archives-ouvertes.fr/hal-00777381
Concentration inequalities: A nonasymptotic theory of independence, 2013. ,
URL : https://hal.archives-ouvertes.fr/hal-00794821
Stability and generalization, Journal of machine learning research, vol.2, pp.499-526, 2002. ,
Sharper bounds for uniformly stable algorithms, 2019. ,
Large deviations bounds for estimating conditional value-at-risk, Operations Research Letters, vol.35, issue.6, pp.722-730, 2007. ,
PAC-Bayesian supervised classification: the thermodynamics of statistical learning, Lecture Notes-Monograph Series. IMS, 2007. ,
URL : https://hal.archives-ouvertes.fr/hal-00206119
, Stability revisited: new generalisation bounds for the leave-oneout, 2016.
Prediction, learning, and games, 2006. ,
A Risk-Averse Newsvendor Model Under the CVaR Criterion, Operations Research, vol.57, issue.4, pp.1040-1044, 2009. ,
Algorithms for CVaR Optimization in MDPs, Advances in Neural Information Processing Systems, vol.27, pp.3509-3517, 2014. ,
I-divergence geometry of probability distributions and minimization problems, Annals of Probability, vol.3, pp.146-158, 1975. ,
Asymptotic evaluation of certain Markov process expectations for large time -III, Communications on pure and applied Mathematics, vol.29, issue.4, pp.389-461, 1976. ,
Learning models with uniform performance via distributionally robust optimization, 2018. ,
Risk, ambiguity, and the savage axioms. The quarterly journal of economics, pp.643-669, 1961. ,
, A Primer on PAC-Bayesian Learning. arXiv, 2019.
URL : https://hal.archives-ouvertes.fr/hal-01983732
Risk-aware multi-armed bandit problem with application to portfolio selection, Royal Society Open Science, vol.4, issue.11, 2017. ,
Concentration bounds for empirical conditional value-at-risk: The unbounded case, Operations Research Letters, vol.47, issue.1, pp.16-20, 2019. ,
PAC-Bayes & margins, Advances in Neural Information Processing Systems, pp.439-446, 2003. ,
A note on the PAC-Bayesian theorem, 2004. ,
Empirical Bernstein bounds and sample variance penalization, Proceedings COLT 2009, 2009. ,
PAC-Bayesian Stochastic Model Selection, Machine Learning, vol.51, pp.5-21, 2003. ,
Concentration, Probabilistic methods for algorithmic discrete mathematics, pp.195-248, 1998. ,
PAC-Bayes Un-Expected Bernstein Inequality, Advances in Neural Information Processing Systems, pp.12180-12191, 2019. ,
URL : https://hal.archives-ouvertes.fr/hal-02482355
Nonparametric return distribution approximation for reinforcement learning, Proceedings of the 27th International Conference on International Conference on Machine Learning, pp.799-806, 2010. ,
Variance-based regularization with convex objectives, Advances in Neural Information Processing Systems, pp.2971-2980, 2017. ,
Some Remarks on the Value-at-Risk and the Conditional Value-at-Risk, pp.272-281, 2000. ,
Robust adversarial reinforcement learning, Proceedings of the 34th International Conference on Machine Learning, vol.70, pp.2817-2826, 2017. ,
Actor-critic algorithms for risk-sensitive MDPs, Advances in neural information processing systems, pp.252-260, 2013. ,
The fundamental risk quadrangle in risk management, optimization and statistical estimation, vol.18, pp.33-53, 2013. ,
Optimization of conditional value-at-risk, Journal of Risk, vol.2, issue.3, pp.21-41, 2000. ,
PAC-Bayesian generalization error bounds for Gaussian process classification, Journal of Machine Learning Research, vol.3, pp.233-269, 2002. ,
A robust approach based on conditional value-at-risk measure to statistical learning problems, European Journal of Operational Research, vol.198, issue.1, pp.287-296, 2009. ,
?-support vector machine as conditional value-at-risk minimization, Proceedings of the 25th international conference on Machine learning, pp.1056-1063, 2008. ,
Optimizing the CVaR via sampling, Twenty-Ninth AAAI Conference on Artificial Intelligence, 2015. ,
Concentration inequalities for conditional value at risk, Proceedings of the 36th International Conference on Machine Learning, vol.97, pp.9-15, 2019. ,
Pac-bayes-empirical-bernstein inequality, Advances in Neural Information Processing Systems 26: 27th Annual Conference on Neural Information Processing Systems 2013. Proceedings of a meeting held, pp.109-117, 2013. ,
, High-Dimensional Statistics: A Non-Asymptotic Viewpoint. Cambridge Series in Statistical and Probabilistic Mathematics, 2019.
Deviation inequalities for an estimator of the conditional value-at-risk, Operations Research Letters, vol.38, issue.3, pp.236-239, 2010. ,
Fairness risk measures, International Conference on Machine Learning, pp.6786-6797, 2019. ,
We say that R? L 1 (?) ? R ? {+?} is a coherent risk measure if, for any Z, Z ? ? L 1 (?) and c ? R, it satisfies the following axioms: (Positive Homogeneity) R[?Z] = ?R ,
, It is known that the conditional value at risk is a member of a class of CRMs called ?-entropic risk measures Ahmadi-Javid, 2012.
, These CRMs are often used in the context of robust optimization Namkoong and Duchi, 2017.