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This paper proposes a new reinforcement learning with hyperbolic discounting. Combining a new temporal difference error with the hyperbolic discounting in recursive manner and reward-punishment framework, a new scheme to learn the optimal…

Machine Learning · Computer Science 2021-06-04 Taisuke Kobayashi

Reinforcement learning (RL) typically defines a discount factor as part of the Markov Decision Process. The discount factor values future rewards by an exponential scheme that leads to theoretical convergence guarantees of the Bellman…

Machine Learning · Statistics 2019-03-01 William Fedus , Carles Gelada , Yoshua Bengio , Marc G. Bellemare , Hugo Larochelle

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

Distributional reinforcement learning (RL) is a powerful framework increasingly adopted in safety-critical domains for its ability to optimize risk-sensitive objectives. However, the role of the discount factor is often overlooked, as it is…

Machine Learning · Computer Science 2026-02-05 Mehrdad Moghimi , Anthony Coache , Hyejin Ku

The endeavor of artificial intelligence (AI) is to design autonomous agents capable of achieving complex tasks. Namely, reinforcement learning (RL) proposes a theoretical background to learn optimal behaviors. In practice, RL algorithms…

Machine Learning · Computer Science 2022-09-27 Firas Jarboui , Ahmed Akakzia

Reinforcement learning has traditionally been studied with exponential discounting or the average reward setup, mainly due to their mathematical tractability. However, such frameworks fall short of accurately capturing human behavior, which…

Machine Learning · Computer Science 2024-09-18 S. R. Eshwar , Mayank Motwani , Nibedita Roy , Gugan Thoppe

Continuous-time reinforcement learning offers an appealing formalism for describing control problems in which the passage of time is not naturally divided into discrete increments. Here we consider the problem of predicting the distribution…

Machine Learning · Computer Science 2022-06-20 Harley Wiltzer , David Meger , Marc G. Bellemare

In reinforcement learning (RL), the goal is to obtain an optimal policy, for which the optimality criterion is fundamentally important. Two major optimality criteria are average and discounted rewards. While the latter is more popular, it…

Machine Learning · Computer Science 2022-09-05 Vektor Dewanto , Marcus Gallagher

This paper studies the optimal dividend problem with a bounded payout rate in a partially observed regime-switching diffusion model, where, in practice, the market regime is unobserved and key model parameters are unknown. To address this…

Optimization and Control · Mathematics 2026-01-29 Zhongqin Gao , Yan Lv , Jingmin He

Discounted reinforcement learning is fundamentally incompatible with function approximation for control in continuing tasks. It is not an optimization problem in its usual formulation, so when using function approximation there is no…

Artificial Intelligence · Computer Science 2019-11-28 Abhishek Naik , Roshan Shariff , Niko Yasui , Hengshuai Yao , Richard S. Sutton

The problem of reinforcement learning is considered where the environment or the model undergoes a change. An algorithm is proposed that an agent can apply in such a problem to achieve the optimal long-time discounted reward. The algorithm…

Systems and Control · Electrical Eng. & Systems 2023-04-25 Wuxia Chen , Taposh Banerjee , Jemin George , Carl Busart

For continuous systems modeled by dynamical equations such as ODEs and SDEs, Bellman's Principle of Optimality takes the form of the Hamilton-Jacobi-Bellman (HJB) equation, which provides the theoretical target of reinforcement learning…

Machine Learning · Computer Science 2025-10-28 Haruki Settai , Naoya Takeishi , Takehisa Yairi

Reinforcement learning (RL) agents have traditionally been tasked with maximizing the value function of a Markov decision process (MDP), either in continuous settings, with fixed discount factor $\gamma < 1$, or in episodic settings, with…

Machine Learning · Computer Science 2019-02-11 Silviu Pitis

Reinforcement learning (RL) for exponential-utility optimization in discounted Markov decision processes (MDPs) lacks principled value-based algorithms. We address this gap in the fixed risk-aversion setting. Building on the Bellman-type…

Machine Learning · Computer Science 2026-05-11 Gugan Thoppe , L. A. Prashanth , Ankur Naskar , Sanjay Bhat

Reinforcement learning algorithms describe how an agent can learn an optimal action policy in a sequential decision process, through repeated experience. In a given environment, the agent policy provides him some running and terminal…

Theoretical Economics · Economics 2020-03-24 Arthur Charpentier , Romuald Elie , Carl Remlinger

Designing an effective reward function has long been a challenge in reinforcement learning, particularly for complex tasks in unstructured environments. To address this, various learning paradigms have emerged that leverage different forms…

Machine Learning · Computer Science 2025-04-29 Muhammad Qasim Elahi , Somtochukwu Oguchienti , Maheed H. Ahmed , Mahsa Ghasemi

The aim of inverse reinforcement learning (IRL) is to infer an agent's preferences from observing their behaviour. Usually, preferences are modelled as a reward function, $R$, and behaviour is modelled as a policy, $\pi$. One of the central…

Machine Learning · Computer Science 2024-12-17 Joar Skalse , Alessandro Abate

Preference-based Reinforcement Learning (PbRL) replaces reward values in traditional reinforcement learning by preferences to better elicit human opinion on the target objective, especially when numerical reward values are hard to design or…

Machine Learning · Computer Science 2020-10-27 Yichong Xu , Ruosong Wang , Lin F. Yang , Aarti Singh , Artur Dubrawski

This paper investigates the so-called reward-balancing methods, a novel class of algorithms for solving discounted-return reinforcement learning (RL) problems. These methods consist of iteratively adjusting the reward function to transform…

Optimization and Control · Mathematics 2026-04-23 Simone Baroncini , Bahman Gharesifard , Giuseppe Notarstefano

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
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