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We study online learning in episodic finite-horizon Markov decision processes (MDPs) with convex objective functions, known as the concave utility reinforcement learning (CURL) problem. This setting generalizes RL from linear to convex…

Machine Learning · Computer Science 2025-05-13 Bianca Marin Moreno , Khaled Eldowa , Pierre Gaillard , Margaux Brégère , Nadia Oudjane

Many machine learning tasks can be solved by minimizing a convex function of an occupancy measure over the policies that generate them. These include reinforcement learning, imitation learning, among others. This more general paradigm is…

Optimization and Control · Mathematics 2023-12-01 Bianca Marin Moreno , Margaux Brégère , Pierre Gaillard , Nadia Oudjane

We consider inverse reinforcement learning problems with concave utilities. Concave Utility Reinforcement Learning (CURL) is a generalisation of the standard RL objective, which employs a concave function of the state occupancy measure,…

Machine Learning · Computer Science 2024-08-05 Mustafa Mert Çelikok , Frans A. Oliehoek , Jan-Willem van de Meent

We explore online learning in episodic loop-free Markov decision processes on non-stationary environments (changing losses and probability transitions). Our focus is on the Concave Utility Reinforcement Learning problem (CURL), an extension…

Machine Learning · Computer Science 2024-05-31 Bianca Marin Moreno , Margaux Brégère , Pierre Gaillard , Nadia Oudjane

This paper studies the safe reinforcement learning problem formulated as an episodic finite-horizon tabular constrained Markov decision process with an unknown transition kernel and stochastic reward and cost functions. We propose a…

Machine Learning · Computer Science 2024-10-15 Kihyun Yu , Duksang Lee , William Overman , Dabeen Lee

We study the constrained reinforcement learning problem, in which an agent aims to maximize the expected cumulative reward subject to a constraint on the expected total value of a utility function. In contrast to existing model-based…

Machine Learning · Computer Science 2023-01-10 Arnob Ghosh , Xingyu Zhou , Ness Shroff

Concave Utility Reinforcement Learning (CURL) extends RL from linear to concave utilities in the occupancy measure induced by the agent's policy. This encompasses not only RL but also imitation learning and exploration, among others. Yet,…

This paper presents an inverse optimal control methodology and its application to training a predictive model of human motor control from a manipulation task. It introduces a convex formulation for learning both objective function and…

Systems and Control · Computer Science 2019-12-05 Marcel Menner , Peter Worsnop , Melanie N. Zeilinger

To tackle long planning horizon problems in reinforcement learning with general function approximation, we propose the first algorithm, termed as UCRL-WVTR, that achieves both \emph{horizon-free} and \emph{instance-dependent}, since it…

Machine Learning · Computer Science 2023-12-08 Jiayi Huang , Han Zhong , Liwei Wang , Lin F. Yang

This paper proposes a reinforcement learning (RL) algorithm for infinite horizon $\rm {H_{2}/H_{\infty}}$ problem in a class of stochastic discrete-time systems, rather than using a set of coupled generalized algebraic Riccati equations…

Optimization and Control · Mathematics 2023-11-28 Xiushan Jiang , Li Wang , Dongya Zhao , Ling Shi

We develop a probabilistic framework for analysing model-based reinforcement learning in the episodic setting. We then apply it to study finite-time horizon stochastic control problems with linear dynamics but unknown coefficients and…

Machine Learning · Computer Science 2021-12-22 Lukasz Szpruch , Tanut Treetanthiploet , Yufei Zhang

Convex Q-learning is a recent approach to reinforcement learning, motivated by the possibility of a firmer theory for convergence, and the possibility of making use of greater a priori knowledge regarding policy or value function structure.…

Optimization and Control · Mathematics 2022-10-18 Fan Lu , Joel Mathias , Sean Meyn , Karanjit Kalsi

We study reinforcement learning (RL) for a class of continuous-time linear-quadratic (LQ) control problems for diffusions, where states are scalar-valued and running control rewards are absent but volatilities of the state processes depend…

Machine Learning · Computer Science 2025-07-25 Yilie Huang , Yanwei Jia , Xun Yu Zhou

We study Constrained Online Convex Optimization (COCO), where a learner chooses actions iteratively, observes both unanticipated convex loss and convex constraint, and accumulates loss while incurring penalties for constraint violations. We…

Machine Learning · Computer Science 2026-01-27 Ricardo N. Ferreira , João Xavier , Cláudia Soares

Constrained Markov Decision Processes are a class of stochastic decision problems in which the decision maker must select a policy that satisfies auxiliary cost constraints. This paper extends upper confidence reinforcement learning for…

Machine Learning · Computer Science 2020-01-28 Liyuan Zheng , Lillian J. Ratliff

We address the problem of simultaneously learning and control in an online receding horizon control setting. We consider the control of an unknown linear dynamical system with general cost functions and affine constraints on the control…

Optimization and Control · Mathematics 2022-11-02 Deepan Muthirayan , Jianjun Yuan , Pramod P. Khargonekar

We consider the finite horizon continuous reinforcement learning problem. Our contribution is three-fold. First,we give a tractable algorithm based on optimistic value iteration for the problem. Next,we give a lower bound on regret of order…

Machine Learning · Computer Science 2019-08-05 Phanideep Gampa , Sairam Satwik Kondamudi , Lakshmanan Kailasam

Recently, adversarial imitation learning has shown a scalable reward acquisition method for inverse reinforcement learning (IRL) problems. However, estimated reward signals often become uncertain and fail to train a reliable statistical…

Machine Learning · Computer Science 2023-01-06 Dong-Sig Han , Hyunseo Kim , Hyundo Lee , Je-Hwan Ryu , Byoung-Tak Zhang

This paper considers online convex optimization with long term constraints, where constraints can be violated in intermediate rounds, but need to be satisfied in the long run. The cumulative constraint violation is used as the metric to…

Machine Learning · Computer Science 2021-06-10 Xinlei Yi , Xiuxian Li , Tao Yang , Lihua Xie , Tianyou Chai , Karl H. Johansson

Understanding how to efficiently learn while adhering to safety constraints is essential for using online reinforcement learning in practical applications. However, proving rigorous regret bounds for safety-constrained reinforcement…

Machine Learning · Statistics 2025-04-29 Benjamin Schiffer , Lucas Janson
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