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This paper establishes a rigorous connection between regularized discrete-time reinforcement learning (RL) and continuous-time stochastic optimal control. Specifically, classical RL algorithms are typically solving a regularized…

Optimization and Control · Mathematics 2026-04-24 Huyên Pham , Yuming Paul Zhang , Yuhua Zhu

Reinforcement learning (RL) is currently one of the most prominent methods for optimizing dynamical systems, with breakthrough results across various fields. The framework is based on the concept of a Markov decision process (MDP), leading…

Optimization and Control · Mathematics 2025-11-17 Rene Carmona , Mathieu Lauriere

Temporal difference (TD) learning is a cornerstone reinforcement learning (RL) method for policy evaluation, where the goal is to estimate the value function of a Markov decision process under a fixed policy. While a substantial body of…

Machine Learning · Computer Science 2026-02-02 Donghwan Lee , Do Wan Kim

One of the main goals of reinforcement learning (RL) is to provide a~way for physical machines to learn optimal behavior instead of being programmed. However, effective control of the machines usually requires fine time discretization. The…

Machine Learning · Computer Science 2022-07-12 Jakub Łyskawa , Paweł Wawrzyński

Reinforcement learning (RL) excels in optimizing policies for discrete-time Markov decision processes (MDP). However, various systems are inherently continuous in time, making discrete-time MDPs an inexact modeling choice. In many…

Machine Learning · Computer Science 2024-11-01 Lenart Treven , Bhavya Sukhija , Yarden As , Florian Dörfler , Andreas Krause

Temporal difference (TD) learning is often used to update the estimate of the value function which is used by RL agents to extract useful policies. In this paper, we focus on value function estimation in continual reinforcement learning. We…

Machine Learning · Computer Science 2023-12-20 Nishanth Anand , Doina Precup

Designing optimal controllers continues to be challenging as systems are becoming complex and are inherently nonlinear. The principal advantage of reinforcement learning (RL) is its ability to learn from the interaction with the environment…

Machine Learning · Computer Science 2018-10-05 Savinay Nagendra , Nikhil Podila , Rashmi Ugarakhod , Koshy George

Reward specification plays a central role in reinforcement learning (RL), guiding the agent's behavior. To express non-Markovian rewards, formalisms such as reward machines have been introduced to capture dependencies on histories. However,…

Artificial Intelligence · Computer Science 2026-05-13 Rajarshi Roy , Anirban Majumdar , Ritam Raha , David Parker , Marta Kwiatkowska

We consider the core reinforcement-learning problem of on-policy value function approximation from a batch of trajectory data, and focus on various issues of Temporal Difference (TD) learning and Monte Carlo (MC) policy evaluation. The two…

Reinforcement learning (RL) has achieved significant success across a wide range of domains, however, most existing methods are formulated in discrete time. In this work, we introduce a novel RL method for continuous-time control, where…

Machine Learning · Computer Science 2025-10-21 Chengxiu Hua , Jiawen Gu , Yushun Tang

We propose a unified framework to study policy evaluation (PE) and the associated temporal difference (TD) methods for reinforcement learning in continuous time and space. We show that PE is equivalent to maintaining the martingale…

Machine Learning · Computer Science 2022-02-02 Yanwei Jia , Xun Yu Zhou

This paper addresses the problem of learning optimal control policies for systems with uncertain dynamics and high-level control objectives specified as Linear Temporal Logic (LTL) formulas. Uncertainty is considered in the workspace…

Robotics · Computer Science 2024-10-17 Yiannis Kantaros , Jun Wang

Constrained Reinforcement Learning (CRL) is a subset of machine learning that introduces constraints into the traditional reinforcement learning (RL) framework. Unlike conventional RL which aims solely to maximize cumulative rewards, CRL…

Artificial Intelligence · Computer Science 2024-12-02 Xiaoshan Lin , Sadık Bera Yüksel , Yasin Yazıcıoğlu , Derya Aksaray

Our understanding of reinforcement learning (RL) has been shaped by theoretical and empirical results that were obtained decades ago using tabular representations and linear function approximators. These results suggest that RL methods that…

Machine Learning · Computer Science 2018-06-05 Artemij Amiranashvili , Alexey Dosovitskiy , Vladlen Koltun , Thomas Brox

Reinforcement learning with verifiable rewards (RLVR) has become a core technique for post-training of Large Language Models (LLMs). While policy optimization is driven by all sampled tokens under a globally broadcast scalar reward, the…

Machine Learning · Computer Science 2026-05-26 Jinghao Zhang , Ruilin Li , Feng Zhao , Jiaqi Wang

We study reinforcement learning (RL) in the setting of continuous time and space, for an infinite horizon with a discounted objective and the underlying dynamics driven by a stochastic differential equation. Built upon recent advances in…

Machine Learning · Computer Science 2023-10-19 Hanyang Zhao , Wenpin Tang , David D. Yao

This paper bridges some of the gap between optimal planning and reinforcement learning (RL), both of which share roots in dynamic programming applied to sequential decision making or optimal control. Whereas planning typically favors…

Robotics · Computer Science 2026-03-10 Filip V. Georgiev , Kalle G. Timperi , Başak Sakçak , Steven M. LaValle

Linear dynamical systems that obey stochastic differential equations are canonical models. While optimal control of known systems has a rich literature, the problem is technically hard under model uncertainty and there are hardly any…

Systems and Control · Electrical Eng. & Systems 2023-06-09 Mohamad Kazem Shirani Faradonbeh , Mohamad Sadegh Shirani Faradonbeh

This paper studies the continuous-time reinforcement learning (RL) for optimal switching problems across multiple regimes. We consider a type of exploratory formulation under entropy regularization where the agent randomizes both the timing…

Optimization and Control · Mathematics 2025-12-23 Yijie Huang , Mengge Li , Xiang Yu , Zhou Zhou

We propose an automata-theoretic approach for reinforcement learning (RL) under complex spatio-temporal constraints with time windows. The problem is formulated using a Markov decision process under a bounded temporal logic constraint.…

Artificial Intelligence · Computer Science 2023-08-01 Xiaoshan Lin , Abbasali Koochakzadeh , Yasin Yazicioglu , Derya Aksaray
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