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In this paper, we consider Markov Decision Processes (MDPs) with error states. Error states are those states entering which is undesirable or dangerous. We define the risk with respect to a policy as the probability of entering such a state…

Machine Learning · Computer Science 2011-09-13 P. Geibel , F. Wysotzki

Model-based offline reinforcement learning (RL) aims to find highly rewarding policy, by leveraging a previously collected static dataset and a dynamics model. While the dynamics model learned through reuse of the static dataset, its…

Machine Learning · Computer Science 2022-11-01 Kaiyang Guo , Yunfeng Shao , Yanhui Geng

This paper studies an optimal investment-reinsurance problem for an insurer (she) under the Cram\'er--Lundberg model with monotone mean--variance (MMV) criterion. At any time, the insurer can purchase reinsurance (or acquire new business)…

Portfolio Management · Quantitative Finance 2024-05-30 Xiaomin Shi , Zuo Quan Xu

Optimal decision making with limited or no information in stochastic environments where multiple agents interact is a challenging topic in the realm of artificial intelligence. Reinforcement learning (RL) is a popular approach for arriving…

Machine Learning · Computer Science 2019-01-08 Roi Ceren

Existing risk-aware multi-armed bandit models typically focus on risk measures of individual options such as variance. As a result, they cannot be directly applied to important real-world online decision making problems with correlated…

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

CVaR (Conditional Value at Risk) is a risk metric widely used in finance. However, dynamically optimizing CVaR is difficult since it is not a standard Markov decision process (MDP) and the principle of dynamic programming fails. In this…

Optimization and Control · Mathematics 2022-10-18 Li Xia , Peter W. Glynn

Reinforcement learning algorithms assume that observations satisfy the Markov property, yet real-world sensors frequently violate this assumption through correlated noise, latency, or partial observability. Standard performance metrics…

Machine Learning · Computer Science 2026-05-08 Naveen Mysore

Value-at-risk (VaR), also known as quantile, is a crucial risk measure in finance and other fields. However, optimizing VaR metrics in Markov decision processes (MDPs) is challenging because VaR is non-additive and the traditional dynamic…

Optimization and Control · Mathematics 2025-07-31 Li Xia , Jinyan Pan

In light of the burgeoning success of reinforcement learning (RL) in diverse real-world applications, considerable focus has been directed towards ensuring RL policies are robust to adversarial attacks during test time. Current approaches…

Machine Learning · Computer Science 2024-02-21 Xiangyu Liu , Chenghao Deng , Yanchao Sun , Yongyuan Liang , Furong Huang

Safe reinforcement learning has been a promising approach for optimizing the policy of an agent that operates in safety-critical applications. In this paper, we propose an algorithm, SNO-MDP, that explores and optimizes Markov decision…

Machine Learning · Computer Science 2020-08-18 Akifumi Wachi , Yanan Sui

Designing optimal reward functions has been desired but extremely difficult in reinforcement learning (RL). When it comes to modern complex tasks, sophisticated reward functions are widely used to simplify policy learning yet even a tiny…

Machine Learning · Computer Science 2021-09-07 Ning Wei , Jiahua Liang , Di Xie , Shiliang Pu

Online learning has traditionally focused on the expected rewards. In this paper, a risk-averse online learning problem under the performance measure of the mean-variance of the rewards is studied. Both the bandit and full information…

Machine Learning · Statistics 2019-03-15 Sattar Vakili , Alexis Boukouvalas , Qing Zhao

Ensuring safety is a critical challenge in applying Reinforcement Learning (RL) to real-world scenarios. Constrained Reinforcement Learning (CRL) addresses this by maximizing returns under predefined constraints, typically formulated as the…

Machine Learning · Computer Science 2026-01-21 Shiqing Gao , Yihang Zhou , Shuai Shao , Haoyu Luo , Yiheng Bing , Jiaxin Ding , Luoyi Fu , Xinbing Wang

We consider the problem of learning models for risk-sensitive reinforcement learning. We theoretically demonstrate that proper value equivalence, a method of learning models which can be used to plan optimally in the risk-neutral setting,…

Machine Learning · Computer Science 2023-12-05 Tyler Kastner , Murat A. Erdogdu , Amir-massoud Farahmand

Reinforcement learning in non-stationary environments is challenging due to abrupt and unpredictable changes in dynamics, often causing traditional algorithms to fail to converge. However, in many real-world cases, non-stationarity has some…

Machine Learning · Computer Science 2025-03-25 Mohsen Amiri , Sindri Magnússon

In dynamic programming (DP) and reinforcement learning (RL), an agent learns to act optimally in terms of expected long-term return by sequentially interacting with its environment modeled by a Markov decision process (MDP). More generally…

Machine Learning · Computer Science 2022-01-03 Mastane Achab , Gergely Neu

We propose a comprehensive framework for policy gradient methods tailored to continuous time reinforcement learning. This is based on the connection between stochastic control problems and randomised problems, enabling applications across…

Optimization and Control · Mathematics 2024-05-01 Robert Denkert , Huyên Pham , Xavier Warin

Learning and optimal control under robust Markov decision processes (MDPs) have received increasing attention, yet most existing theory, algorithms, and applications focus on finite-horizon or discounted models. Long-run average-reward…

Optimization and Control · Mathematics 2025-12-12 Shengbo Wang , Nian Si

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

This paper introduces two metrics (cycle-based and memory-based metrics), grounded on a dynamical game-theoretic solution concept called sink equilibrium, for the evaluation, ranking, and computation of policies in multi-agent learning. We…

Computer Science and Game Theory · Computer Science 2020-06-23 Rui Yan , Xiaoming Duan , Zongying Shi , Yisheng Zhong , Jason R. Marden , Francesco Bullo