Conditional Value-at-Risk

Also known as CVaR

Conditional Value-at-Risk (CVaR) captures the average severity of outcomes beyond a chosen loss quantile, helping decisions account for rare but costly events. Methods use threshold-based optimization, risk-sensitive reinforcement learning and control, distributionally robust estimation, and conformal calibration to manage tail risk. Applications include portfolio selection, safe robotics, and planning under uncertainty, with guarantees studied for learning and policy evaluation. A central challenge is that tail estimates depend on few observations, so quantile errors and distribution shifts can make risk-aware decisions unstable even when the estimator is robust.

Latest papers

27 papers5 papers in the last four weeks, up 67% on the four weeks before. 0.0% of all new papers.

Deep catastrophic-risk-aware reinforcement learning
Oct 19, 2026Carlos Pérez Octavio Mendoza, Frédéric GodinRisk-Sensitive RL Conditional Value-at-Risk
Concordia University, Department of Mathematics and Statistics, Montréal, Canada · Quantact Laboratory, Centre de Recherches Mathématiques, Montréal, Canada
Beyond Expected Values: Risk-Sensitive Planning with Distributional Monte-Carlo Tree Search
Oct 16, 2026Quynh Trinh, Trung Nguyen, Nam Nguyen +1Risk-Sensitive Planning Monte Carlo Tree Search
Hanoi University of Science and Technology, Hanoi, Vietnam · Center for AI Research, VinUniversity, Hanoi, Vietnam
Bayesian Optimization of CVaR with Unknown Hyperparameters
Oct 13, 2026Valentin Margraf, Jonas Hanselle, Viktor Bengs +3Bayesian Optimization Conditional Value-at-Risk
LMU Munich · Munich Center for Machine Learning (MCML) · German Research Center for Artificial Intelligence (DFKI) +3
Credal Machine Learning for Risk-Averse Decision Making
Oct 8, 2026Timo Löhr, Paul Hofman, Maximilian Muschalik +1Decision-Making under Uncertainty Conditional Value-at-Risk
LMU Munich, MCML · LMU Munich, MCML, DFKI
Tail-Influence Sampling for CVaR Policy Evaluation
Sep 29, 2026Pauline Bourigault, Xiaotong Ji, Matthieu Zimmer +2Policy Evaluation Adaptive Sampling
Imperial College London · Huawei Noah’s Ark Lab · UCL Centre for AI
Risk-Averse Online POMDP Planning via CVaR of the Immediate Cost with Performance Guarantees
Sep 26, 2026Yaacov Pariente, Vadim IndelmanRisk-Sensitive Planning Partially Observable Markov Decision Processes
Faculty of Mathematics Technion – Israel Institute of Technology Haifa, Israel · Stephen B. Klein Faculty of Aerospace Engineering; Faculty of Data and Decision Sciences Technion – Israel Institute of Technology Haifa, Israel
CVaR anchor regression protects against rare shifts
Sep 22, 2026Malte LondschienDistribution Shift Robustness Robust Regression
BCPPO: Bachelier-Inspired Constrained Proximal Policy Optimization for Tail-Risk-Aware Safe Reinforcement Learning
Aug 31, 2026Dongsheng Hou, Yanqiao Chen, Yuhan RuiReinforcement Learning Constrained RL
Southern University of Science and Technology
Conformal Risk-Averse Decision Making with Optimized Certainty Equivalent Risk Control
Aug 28, 2026Amirmohammad Farzaneh, Osvaldo SimeoneDecision-Making under Uncertainty Conformal Risk Control
Institute for Intelligent Networked Systems (INSI), Northeastern University London, London, UK
Adaptive Finite-Budget Training for CVaR Risk-Aware Q-Learning
Aug 5, 2026Yifan Wu, Junjie Lei, Wenjie HuangReinforcement Learning Q-Learning
Department of Data and Systems Engineering The University of Hong Kong Hong Kong, Hong Kong SAR
FIRMGrasp: A Friction-Informed Risk Margin for Robust Grasp Synthesis
Jul 27, 2026Clinton Enwerem, John S. Baras, Calin BeltaRobotic Grasping Conditional Value-at-Risk
Department of Electrical & Computer Engineering and Institute for Systems Research, University of Maryland, College Park, MD, USA
Computing Monetary Risk Measures in Linear Time
Jul 6, 2026Palash Agrawal, Gersi Doko, Maeve Burwell +1Quantitative Finance Conditional Value-at-Risk
∗Equal contribution.
Benchmarking Quantum Algorithmic Resilience for CVaR Portfolio Optimization: The Expressibility-Coherence Trade-off
Jun 5, 2026Prashik N. Somkuwar, K. Srinivasan, G. RaghavanVariational Quantum Circuits Portfolio Optimization
School of Quantum Technology, Defence Institute of Advanced Technology, Pune, India
Mitigating Anchoring Bias in LLM-Based Agents for Energy-Efficient 6G Autonomous Networks
Jun 5, 2026Hatim Chergui, Claudia Carballo González, Farhad Rezazadeh +1Multi-Agent LLM Systems 6G Networks
i2CAT Foundation, 08034 Barcelona, Spain · Universitat Polit`ecnica de Catalunya (UPC), 08034 Barcelona, Spain · Research Institute for Digital Future, Khalifa University, 127788 Abu Dhabi, UAE
Adversarially Robust Control of Conditional Value-at-Risk via Rockafellar-Uryasev Conformal Inference
May 29, 2026Catherine Chen, Jingyan Shen, Zhun Deng +1Conformal Risk Control Conditional Value-at-Risk
Institute for Computational and Mathematical Engineering, Stanford University · Department of Computer Science, New York University · Department of Computer Science, University of North Carolina at Chapel Hill +1
On the Sample Complexity of Discounted Reinforcement Learning with Optimized Certainty Equivalents
May 20, 2026Oliver Mortensen, Mohammad Sadegh TalebiReinforcement Learning Risk-Sensitive RL
Department of Computer Science, University of Copenhagen.
DiffCVaR: Reinforcement Learning for Risk Adaptation via Differentiable CVaR Barrier Functions
May 20, 2026Xinyi Wang, Taekyung Kim, Bardh Hoxha +2Control Barrier Functions Risk-Sensitive RL
Department of Robotics, University of Michigan, Ann Arbor, MI, 48109, USA · Toyota Motor North America, Research & Development, Ann Arbor, MI, 48105, USA · Department of Aerospace Engineering, University of Michigan, Ann Arbor, MI, 48109, USA
The Privacy Price of Tail-Risk Learning: Effective Tail Sample Size in Differentially Private CVaR Optimization
May 15, 2026El Mustapha MansouriStochastic Optimization Differential Privacy
School of Engineering, Institute of Science Tokyo, Yokohama, Kanagawa 226-8501, Japan
Actor-Critic Algorithm for Dynamic Expectile and CVaR
May 8, 2026Yudong Luo, Erick DelageReinforcement Learning Risk-Sensitive RL
1GERAD & Department of Decision Sciences, HEC Montr´eal, Canada · 2Mila - Quebec AI Institute, Canada
Wasserstein Distributionally Robust Risk-Sensitive Estimation via Conditional Value-at-Risk
Apr 20, 2026Feras Al Taha, Eilyan BitarDistributionally Robust Optimization Wasserstein Distributionally Robust Optimization
School of Electrical and Computer Engineering, Cornell University, Ithaca, NY 14853 USA
Instantiating Bayesian CVaR lower bounds in Interactive Decision Making Problems
Apr 14, 2026Raghav Bongole, Tobias J. Oechtering, Mikael SkoglundGaussian Process Bandits Decision-Making under Uncertainty
Department of Information Science and Engineering (ISE), KTH Royal Institute of Technology
Risk-Constrained Belief-Space Optimization for Safe Control under Latent Uncertainty
Apr 4, 2026Clinton Enwerem, John S. Baras, Calin BeltaBelief-Space Planning Safety-Critical Control
Institute for Systems Research, University of Maryland, College Park, MD, USA
Adaptive Conditional Residual Sampling for Spectral Risk Optimisation under Decision-Dependent Uncertainty
Mar 12, 2026Marcell T. KurbuczStochastic Optimization Decision-Making under Uncertainty
Institute for Global Prosperity, The Bartlett, University College London, 9–11 Endsleigh Gardens, London, WC1H 0EH, United Kingdom
Accelerated Online Risk-Averse Policy Evaluation in POMDPs with Theoretical Guarantees and Novel CVaR Bounds
Feb 26, 2026Yaacov Pariente, Vadim IndelmanPartially Observable Markov Decision Processes Policy Evaluation
Technion - Israel Institute of Technology, Israel
On the Generalization and Robustness in Conditional Value-at-Risk
Feb 20, 2026Dinesh Karthik Mulumudi, Piyushi Manupriya, Gholamali Aminian +1Conditional Value-at-Risk Empirical Risk Minimization
Dept. of Mathematics, IISER, Pune. · Dept. of Computer Science and Automation, Indian Institute of Sciecne, Bangalore. · The Alan Turing Institute, Greater London, England, UK.
Reward Redistribution for CVaR MDPs using a Bellman Operator on L-infinity
Feb 3, 2026Aneri Muni, Vincent Taboga, Esther Derman +2Markov Decision Processes Q-Learning
Universit´e de Montr´eal, Quebec, Canada · Mila - Quebec AI Institute, Quebec, Canada · GERAD & Department of Decision Sciences, HEC Montr´eal, Quebec, Canada
Risk-averse learning with delayed feedback
Sep 25, 2024Siyi Wang, Zifan Wang, Karl Henrik Johansson +1Dynamic Regret Minimization Zeroth-Order Optimization
Division of Decision and Control Systems, School of Electrical Engineering and Computer Science, KTH Royal Institute of Technology, 10044 Stockholm, Sweden · Chair of Information-oriented Control (ITR), Technical University of Munich, Germany

Oct 19, 2026J/K move · Enter open · S save

Deep catastrophic-risk-aware reinforcement learning

Carlos Pérez Octavio Mendoza, Frédéric Godin

Concordia University, Department of Mathematics and Statistics, Montréal, Canada · Quantact Laboratory, Centre de Recherches Mathématiques, Montréal, Canada

Risk-Sensitive RL Conditional Value-at-Risk Extreme Value Theory Quantitative Finance

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Estimating extreme risk in reinforcement learning becomes increasingly difficult as the confidence level increases, since only a small number of observations contribute to empirical estimates of Conditional Value-at-Risk (CVaR). In this paper, we extend an Extreme Value Theory (EVT) approach for CVaR optimization to high-dimensional neural-network policies. Using a peaks-over-threshold representation and method-of-moments estimation, we obtain a differentiable tail-risk objective and show that, conditional on the selected threshold, its finite-sample gradient can be computed directly through automatic differentiation. We first validate the approach in a controlled experiment with a known optimal solution and then investigate its performance in a deep-hedging problem with rare extreme market movements. Our results show similar hedging behavior for EVT- and empirical-CVaR-trained policies under normal conditions, while EVT-trained policies exhibit lower hedging losses under the extreme-scenario evaluation across the training sample sizes considered. These results suggest that EVT can provide a practical alternative for training neural policies when the observations relevant to extreme risk are scarce.