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This paper addresses the challenge of time-inconsistent stochastic control within a continuous-time framework. Its primary focus lies in uncovering a probabilistic representation, specifically in the shape of a system of backward stochastic…

Optimization and Control · Mathematics 2026-03-24 Dylan Possamaï , Mateo Rodriguez Polo

The theory of continuous-time reinforcement learning (RL) has progressed rapidly in recent years. While the ultimate objective of RL is typically to learn deterministic control policies, most existing continuous-time RL methods rely on…

Machine Learning · Computer Science 2026-03-17 Ziheng Cheng , Xin Guo , Yufei Zhang

Reinforcement learning (RL) algorithms allow artificial agents to improve their selection of actions to increase rewarding experiences in their environments. Temporal Difference (TD) Learning -- a model-free RL method -- is a leading…

Machine Learning · Computer Science 2019-09-05 Jacob Rafati , David C. Noelle

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

Rewards and punishments in different forms are pervasive and present in a wide variety of decision-making scenarios. By observing the outcome of a sufficient number of repeated trials, one would gradually learn the value and usefulness of a…

Machine Learning · Computer Science 2019-06-25 Nikki Lijing Kuang , Clement H. C. Leung

To accumulate knowledge and improve its policy of behaviour, a reinforcement learning agent can learn `off-policy' about policies that differ from the policy used to generate its experience. This is important to learn counterfactuals, or…

Machine Learning · Computer Science 2022-02-03 Simon Schmitt , John Shawe-Taylor , Hado van Hasselt

Temporal-difference (TD) learning is highly effective at controlling and evaluating an agent's long-term outcomes. Most approaches in this paradigm implement a semi-gradient update to boost the learning speed, which consists of ignoring the…

Machine Learning · Computer Science 2026-05-15 Théo Vincent , Kevin Gerhardt , Yogesh Tripathi , Habib Maraqten , Adam White , Martha White , Jan Peters , Carlo D'Eramo

Model-based reinforcement learning (MBRL) approaches rely on discrete-time state transition models whereas physical systems and the vast majority of control tasks operate in continuous-time. To avoid time-discretization approximation of the…

Machine Learning · Computer Science 2021-06-14 Çağatay Yıldız , Markus Heinonen , Harri Lähdesmäki

In a broad class of reinforcement learning applications, stochastic rewards have heavy-tailed distributions, which lead to infinite second-order moments for stochastic (semi)gradients in policy evaluation and direct policy optimization. In…

Machine Learning · Computer Science 2023-06-21 Semih Cayci , Atilla Eryilmaz

Learning auxiliary tasks, such as multiple predictions about the world, can provide many benefits to reinforcement learning systems. A variety of off-policy learning algorithms have been developed to learn such predictions, but as yet there…

Machine Learning · Computer Science 2022-02-24 Matthew McLeod , Chunlok Lo , Matthew Schlegel , Andrew Jacobsen , Raksha Kumaraswamy , Martha White , Adam White

We compare two approaches to the predictive modeling of dynamical systems from partial observations at discrete times. The first is continuous in time, where one uses data to infer a model in the form of stochastic differential equations,…

Numerical Analysis · Mathematics 2017-02-08 Fei Lu , Kevin K. Lin , Alexandre J. Chorin

This work advances the theoretical foundations of reservoir computing (RC) by providing a unified treatment of fading memory and the echo state property (ESP) in both deterministic and stochastic settings. We investigate state-space…

Machine Learning · Statistics 2026-05-15 Juan-Pablo Ortega , Florian Rossmannek

While there are convergence guarantees for temporal difference (TD) learning when using linear function approximators, the situation for nonlinear models is far less understood, and divergent examples are known. Here we take a first step…

Machine Learning · Computer Science 2020-02-12 David Brandfonbrener , Joan Bruna

Reinforcement learning algorithms typically rely on the assumption that the environment dynamics and value function can be expressed in terms of a Markovian state representation. However, when state information is only partially observable,…

In this paper, we introduce proximal gradient temporal difference learning, which provides a principled way of designing and analyzing true stochastic gradient temporal difference learning algorithms. We show how gradient TD (GTD)…

Machine Learning · Computer Science 2020-06-09 Bo Liu , Ian Gemp , Mohammad Ghavamzadeh , Ji Liu , Sridhar Mahadevan , Marek Petrik

We analyse quantile temporal-difference learning (QTD), a distributional reinforcement learning algorithm that has proven to be a key component in several successful large-scale applications of reinforcement learning. Despite these…

We propose and analyze an alternate approach to off-policy multi-step temporal difference learning, in which off-policy returns are corrected with the current Q-function in terms of rewards, rather than with the target policy in terms of…

Artificial Intelligence · Computer Science 2016-08-12 Anna Harutyunyan , Marc G. Bellemare , Tom Stepleton , Remi Munos

Temporal-difference learning with gradient correction (TDC) is a two time-scale algorithm for policy evaluation in reinforcement learning. This algorithm was initially proposed with linear function approximation, and was later extended to…

Machine Learning · Computer Science 2021-10-29 Yue Wang , Shaofeng Zou , Yi Zhou

Treatment effects of stochastic policy shifts quantify differences in outcomes across counterfactual scenarios with varying treatment distributions. Stochastic policy shifts may be of interest in settings where it is unrealistic or…

Methodology · Statistics 2026-03-31 Michael Jetsupphasuk , Chenwei Fang , Didong Li , Michael G. Hudgens

Recent advances in stochastic differential equations (SDEs) have enabled robust modeling of real-world dynamical processes across diverse domains, such as finance, health, and systems biology. However, parameter estimation for SDEs…

Machine Learning · Computer Science 2026-01-29 Long Van Tran , Truyen Tran , Phuoc Nguyen