We study learning algorithms that seek to minimize the conditional value-at-risk (CVaR), when all the learner knows is that the losses incurred may be heavy-tailed. We begin by studying a general-purpose estimator of CVaR for potentially heavy-tailed random variables, which is easy to implement in practice, and requires nothing more than finite variance and a distribution function that does not change too fast or slow around just the quantile of interest. With this estimator in hand, we then derive a new learning algorithm which robustly chooses among candidates produced by stochastic gradient-driven sub-processes. For this procedure we provide high-probability excess CVaR bounds, and to complement the theory we conduct empirical tests of the underlying CVaR estimator and the learning algorithm derived from it.
Stabilized Maximum-Likelihood Iterative Quantum Amplitude Estimation for Structural CVaR under Correlated Random Fields
Department of Mechanical Engineering（机械工程系）；Engineering Science, The University of North Carolina at Charlotte, Charlotte, NC 28223, USA（工程科学，北卡罗来纳大学夏洛特分校）；School of Data Science, The University of North Carolina at Charlotte, Charlotte, NC 28223, USA（数据科学学院）
On the Generalization and Robustness in Conditional Value-at-Risk
Dept. of Mathematics IISER, Pune（数学系，印度科学研究所，普恩）；Dept. of Computer Science and Automation Indian Institute of Sciecne, Bangalore（计算机科学与自动化系，印度科学研究院，班加罗尔）；The Alan Turing Institute Greater London, England, UK（艾伦·图灵研究所，伦敦，英格兰，英国）
LTCI, Télécom Paris, Institut Polytechnique de Paris（巴黎电信学院，巴黎理工学院）；Université Paris Cité, Université Paris Saclay, ENS Paris Saclay, CNRS, SSA, INSERM, Centre Borelli（巴黎西岱大学，巴黎萨克雷大学，巴黎高等师范学校巴黎萨克雷分校，法国国家科学研究中心，SSA，INSERM，博尔莱中心）
