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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

When optimising for conditional value at risk (CVaR) using policy gradients (PG), current methods rely on discarding a large proportion of trajectories, resulting in poor sample efficiency. We propose a reformulation of the CVaR…

Machine Learning · Computer Science 2025-07-22 Harry Mead , Clarissa Costen , Bruno Lacerda , Nick Hawes

In order to model risk aversion in reinforcement learning, an emerging line of research adapts familiar algorithms to optimize coherent risk functionals, a class that includes conditional value-at-risk (CVaR). Because optimizing the…

Machine Learning · Computer Science 2021-03-09 Audrey Huang , Liu Leqi , Zachary C. Lipton , Kamyar Azizzadenesheli

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

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

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

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

Effective reinforcement learning (RL) for complex stochastic systems requires leveraging historical data collected in previous iterations to accelerate policy optimization. Classical experience replay treats all past observations uniformly…

Machine Learning · Statistics 2026-02-06 Hua Zheng , Wei Xie , M. Ben Feng , Keilung Choy

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

We study a risk-constrained version of the stochastic shortest path (SSP) problem, where the risk measure considered is Conditional Value-at-Risk (CVaR). We propose two algorithms that obtain a locally risk-optimal policy by employing four…

Machine Learning · Statistics 2018-10-23 Prashanth L. A.

In this work, we address risk-averse Bayes-adaptive reinforcement learning. We pose the problem of optimising the conditional value at risk (CVaR) of the total return in Bayes-adaptive Markov decision processes (MDPs). We show that a policy…

Machine Learning · Computer Science 2021-10-27 Marc Rigter , Bruno Lacerda , Nick Hawes

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

It was recently shown that dynamic programming (DP) methods for finding static CVaR-optimal policies in Markov Decision Processes (MDPs) can fail when based on the dual formulation, yet the root cause of this failure remains unclear. We…

Machine Learning · Computer Science 2026-04-16 Mathieu Godbout , Audrey Durand

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…

Machine Learning · Statistics 2020-06-04 Matthew J. Holland , El Mehdi Haress

We study a first-order primal-dual subgradient method to optimize risk-constrained risk-penalized optimization problems, where risk is modeled via the popular conditional value at risk (CVaR) measure. The algorithm processes independent and…

Optimization and Control · Mathematics 2021-09-03 Avinash N. Madavan , Subhonmesh Bose

This paper addresses risk averse constrained optimization problems where the objective and constraint functions can only be computed by a blackbox subject to unknown uncertainties. To handle mixed aleatory/epistemic uncertainties, the…

Optimization and Control · Mathematics 2023-10-18 Charles Audet , Jean Bigeon , Romain Couderc , Michael Kokkolaras

In this paper, we revisit and improve the convergence of policy gradient (PG), natural PG (NPG) methods, and their variance-reduced variants, under general smooth policy parametrizations. More specifically, with the Fisher information…

Machine Learning · Computer Science 2022-11-17 Yanli Liu , Kaiqing Zhang , Tamer Başar , Wotao Yin

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

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

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
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