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Conditional Value-at-Risk (CVaR) is a widely used risk-sensitive objective for learning under rare but high-impact losses, yet its statistical behavior under heavy-tailed data remains poorly understood. Unlike expectation-based risk, CVaR…

Machine Learning · Statistics 2026-02-23 Dinesh Karthik Mulumudi , Piyushi Manupriya , Gholamali Aminian , Anant Raj

We propose a risk-averse statistical learning framework wherein the performance of a learning algorithm is evaluated by the conditional value-at-risk (CVaR) of losses rather than the expected loss. We devise algorithms based on stochastic…

Machine Learning · Computer Science 2020-02-17 Tasuku Soma , Yuichi Yoshida

Conditional Value-at-Risk (CVaR) is a widely used risk metric in applications such as finance. We derive concentration bounds for CVaR estimates, considering separately the cases of light-tailed and heavy-tailed distributions. In the…

Machine Learning · Computer Science 2019-08-27 Prashanth L. A. , Krishna Jagannathan , Ravi Kumar Kolla

Data in the real-world classification problems are always imbalanced or long-tailed, wherein the majority classes have the most of the samples that dominate the model training. In such setting, the naive model tends to have poor performance…

Machine Learning · Computer Science 2023-08-30 Hong Zhu , Runpeng Yu , Xing Tang , Yifei Wang , Yuan Fang , Yisen Wang

Options are generally learned by using an inaccurate environment model (or simulator), which contains uncertain model parameters. While there are several methods to learn options that are robust against the uncertainty of model parameters,…

Machine Learning · Computer Science 2019-11-01 Takuya Hiraoka , Takahisa Imagawa , Tatsuya Mori , Takashi Onishi , Yoshimasa Tsuruoka

Motivated by the prominence of Conditional Value-at-Risk (CVaR) as a measure for tail risk in settings affected by uncertainty, we develop a new formula for approximating CVaR based optimization objectives and their gradients from limited…

Methodology · Statistics 2020-08-25 Anand Deo , Karthyek Murthy

Many modern machine learning tasks require models with high tail performance, i.e. high performance over the worst-off samples in the dataset. This problem has been widely studied in fields such as algorithmic fairness, class imbalance, and…

Machine Learning · Computer Science 2021-11-11 Runtian Zhai , Chen Dan , Arun Sai Suggala , Zico Kolter , Pradeep Ravikumar

Conditional Value at Risk (CVaR) is a prominent risk measure that is being used extensively in various domains. We develop a new formula for the gradient of the CVaR in the form of a conditional expectation. Based on this formula, we…

Machine Learning · Statistics 2014-11-25 Aviv Tamar , Yonatan Glassner , Shie Mannor

In a wide variety of sequential decision making problems, it can be important to estimate the impact of rare events in order to minimize risk exposure. A popular risk measure is the conditional value-at-risk (CVaR), which is commonly…

Machine Learning · Statistics 2020-12-11 Dylan Troop , Frédéric Godin , Jia Yuan Yu

In high-stakes machine learning applications, it is crucial to not only perform well on average, but also when restricted to difficult examples. To address this, we consider the problem of training models in a risk-averse manner. We propose…

Machine Learning · Computer Science 2020-11-09 Sebastian Curi , Kfir. Y. Levy , Stefanie Jegelka , Andreas Krause

Distributional reinforcement learning (RL) -- in which agents learn about all the possible long-term consequences of their actions, and not just the expected value -- is of great recent interest. One of the most important affordances of a…

Artificial Intelligence · Computer Science 2021-11-15 Chris Gagne , Peter Dayan

We study risk-sensitive Reinforcement Learning (RL), where we aim to maximize the Conditional Value at Risk (CVaR) with a fixed risk tolerance $\tau$. Prior theoretical work studying risk-sensitive RL focuses on the tabular Markov Decision…

Machine Learning · Computer Science 2023-11-21 Yulai Zhao , Wenhao Zhan , Xiaoyan Hu , Ho-fung Leung , Farzan Farnia , Wen Sun , Jason D. Lee

In many sequential decision-making problems we may want to manage risk by minimizing some measure of variability in costs in addition to minimizing a standard criterion. Conditional value-at-risk (CVaR) is a relatively new risk measure that…

Artificial Intelligence · Computer Science 2014-07-14 Yinlam Chow , Mohammad Ghavamzadeh

Risk-sensitive reinforcement learning (RL) aims to optimize policies that balance the expected reward and risk. In this paper, we present a novel risk-sensitive RL framework that employs an Iterated Conditional Value-at-Risk (CVaR)…

Machine Learning · Computer Science 2023-12-05 Yu Chen , Yihan Du , Pihe Hu , Siwei Wang , Desheng Wu , Longbo Huang

Optimizing Conditional Value-at-risk (CVaR) using policy gradient (a.k.a CVaR-PG) faces significant challenges of sample inefficiency. This inefficiency stems from the fact that it focuses on tail-end performance and overlooks many sampled…

Machine Learning · Computer Science 2026-02-06 Yudong Luo , Erick Delage

Conditional Value-at-Risk (CVaR) is a leading tail-risk measure in finance, central to both regulatory and portfolio optimization frameworks. Classical estimation of CVaR and its gradients relies on Monte Carlo simulation, incurring…

Quantum Physics · Physics 2026-05-19 Vasilis Skarlatos , Nikos Konofaos

Conditional value-at-risk (CVaR) is a prominent risk measure in financial engineering, energy systems, and supply chain management. In these domains, Markov decision processes (MDPs) with a long-run CVaR criterion effectively mitigate cost…

Optimization and Control · Mathematics 2026-03-11 Qixin Wang , Hao Cao , Jian-Qiang Hu , Mingjie Hu , Li Xia

In this paper, we study a novel episodic risk-sensitive Reinforcement Learning (RL) problem, named Iterated CVaR RL, which aims to maximize the tail of the reward-to-go at each step, and focuses on tightly controlling the risk of getting…

Machine Learning · Computer Science 2023-05-12 Yihan Du , Siwei Wang , Longbo Huang

Conditional Value at Risk (CVaR) is a family of "coherent risk measures" which generalize the traditional mathematical expectation. Widely used in mathematical finance, it is garnering increasing interest in machine learning, e.g., as an…

Machine Learning · Computer Science 2020-11-17 Zakaria Mhammedi , Benjamin Guedj , Robert C. Williamson

In real-world scenarios, risk-averse learning is valuable for mitigating potential adverse outcomes. However, the delayed feedback makes it challenging to assess and manage risk effectively. In this paper, we investigate risk-averse…

Machine Learning · Computer Science 2025-08-06 Siyi Wang , Zifan Wang , Karl Henrik Johansson , Sandra Hirche
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