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In this paper we argue for the fundamental importance of the value distribution: the distribution of the random return received by a reinforcement learning agent. This is in contrast to the common approach to reinforcement learning which…

Machine Learning · Computer Science 2017-07-24 Marc G. Bellemare , Will Dabney , Rémi Munos

Many novel notions of "risk" (e.g., CVaR, tilted risk, DRO risk) have been proposed and studied, but these risks are all at least as sensitive as the mean to loss tails on the upside, and tend to ignore deviations on the downside. We study…

Machine Learning · Statistics 2023-02-17 Matthew J. Holland

We propose a novel framework for risk-sensitive reinforcement learning (RSRL) that incorporates robustness against transition uncertainty. We define two distinct yet coupled risk measures: an inner risk measure addressing state and cost…

Risk Management · Quantitative Finance 2026-01-01 Shanyu Han , Yangbo He , Yang Liu

We address the problem of inverse reinforcement learning in Markov decision processes where the agent is risk-sensitive. In particular, we model risk-sensitivity in a reinforcement learning framework by making use of models of human…

Machine Learning · Computer Science 2017-11-23 Lillian J. Ratliff , Eric Mazumdar

Real-world applications require a robot operating in the physical world with awareness of potential risks besides accomplishing the task. A large part of risky behaviors arises from interacting with objects in ignorance of affordance. To…

Robotics · Computer Science 2022-06-28 Meng Song , Yuhan Liu , Zhengqin Li , Manmohan Chandraker

Offline reinforcement learning and offline inverse reinforcement learning aim to recover near-optimal value functions or reward models from a fixed batch of logged trajectories, yet current practice still struggles to enforce Bellman…

Machine Learning · Computer Science 2026-01-27 Enoch H. Kang , Kyoungseok Jang

Inverse optimal control, also known as inverse reinforcement learning, is the problem of recovering an unknown reward function in a Markov decision process from expert demonstrations of the optimal policy. We introduce a probabilistic…

Machine Learning · Computer Science 2012-06-22 Sergey Levine , Vladlen Koltun

We consider the problem of quantifying uncertainty over expected cumulative rewards in model-based reinforcement learning. In particular, we focus on characterizing the variance over values induced by a distribution over Markov decision…

Machine Learning · Computer Science 2024-09-18 Carlos E. Luis , Alessandro G. Bottero , Julia Vinogradska , Felix Berkenkamp , Jan Peters

Solving tasks in Reinforcement Learning is no easy feat. As the goal of the agent is to maximize the accumulated reward, it often learns to exploit loopholes and misspecifications in the reward signal resulting in unwanted behavior. While…

Machine Learning · Computer Science 2018-12-27 Chen Tessler , Daniel J. Mankowitz , Shie Mannor

In online reinforcement learning, data scarcity creates epistemic uncertainty that makes robustness important early in learning, whereas sufficient exploration is needed to learn the true-environment optimal policy. We study this…

Machine Learning · Computer Science 2026-05-26 Meichen Song , Yuhao Wang , Enlu Zhou

Most of reinforcement learning algorithms optimize the discounted criterion which is beneficial to accelerate the convergence and reduce the variance of estimates. Although the discounted criterion is appropriate for certain tasks such as…

Machine Learning · Computer Science 2021-11-02 Xiaoteng Ma , Xiaohang Tang , Li Xia , Jun Yang , Qianchuan Zhao

We derive a family of risk-sensitive reinforcement learning methods for agents, who face sequential decision-making tasks in uncertain environments. By applying a utility function to the temporal difference (TD) error, nonlinear…

Machine Learning · Computer Science 2014-10-10 Yun Shen , Michael J. Tobia , Tobias Sommer , Klaus Obermayer

This paper investigates a novel behavioral feature of recursive preferences: aversion to risks that persist over time, or simply \textit{correlation aversion}. Greater persistence provides information about future consumption but reduces…

Theoretical Economics · Economics 2026-03-24 Lorenzo Maria Stanca

We study risk-sensitive multi-agent reinforcement learning under general-sum Markov games, where agents optimize the entropic risk measure of rewards with possibly diverse risk preferences. We show that using the regret naively adapted from…

Machine Learning · Computer Science 2024-05-07 Yingjie Fei , Ruitu Xu

Learning near-optimal behaviour from an expert's demonstrations typically relies on the assumption that the learner knows the features that the true reward function depends on. In this paper, we study the problem of learning from…

Machine Learning · Computer Science 2019-03-28 Luis Haug , Sebastian Tschiatschek , Adish Singla

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

Fairness plays a crucial role in various multi-agent systems (e.g., communication networks, financial markets, etc.). Many multi-agent dynamical interactions can be cast as Markov Decision Processes (MDPs). While existing research has…

Machine Learning · Computer Science 2023-06-02 Peizhong Ju , Arnob Ghosh , Ness B. Shroff

To apply reinforcement learning to safety-critical applications, we ought to provide safety guarantees during both policy training and deployment. In this work, we present theoretical results that place a bound on the probability of…

Machine Learning · Computer Science 2025-06-24 Jacques Cloete , Nikolaus Vertovec , Alessandro Abate

In this paper, we study a few challenging theoretical and numerical issues on the well known trust region policy optimization for deep reinforcement learning. The goal is to find a policy that maximizes the total expected reward when the…

Optimization and Control · Mathematics 2019-11-27 Mingming Zhao , Yongfeng Li , Zaiwen Wen

We study the sensitivity to estimation error of portfolios optimized under various risk measures, including variance, absolute deviation, expected shortfall and maximal loss. We introduce a measure of portfolio sensitivity and test the…

Physics and Society · Physics 2008-12-02 Imre Kondor , Szilard Pafka , Gabor Nagy