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We present a distributional approach to theoretical analyses of reinforcement learning algorithms for constant step-sizes. We demonstrate its effectiveness by presenting simple and unified proofs of convergence for a variety of…

Machine Learning · Computer Science 2020-03-30 Philip Amortila , Doina Precup , Prakash Panangaden , Marc G. Bellemare

Value function learning plays a central role in many state-of-the-art reinforcement-learning algorithms. Many popular algorithms like Q-learning do not optimize any objective function, but are fixed-point iterations of some variant of…

Machine Learning · Computer Science 2020-01-10 Yihao Feng , Lihong Li , Qiang Liu

Regularized Markov Decision Processes serve as models of sequential decision making under uncertainty wherein the decision maker has limited information processing capacity and/or aversion to model ambiguity. With functional approximation,…

Artificial Intelligence · Computer Science 2025-02-11 Jiachen Xi , Alfredo Garcia , Petar Momcilovic

Many reinforcement learning algorithms rely on value estimation, however, the most widely used algorithms -- namely temporal difference algorithms -- can diverge under both off-policy sampling and nonlinear function approximation. Many…

Machine Learning · Computer Science 2024-08-02 Andrew Patterson , Adam White , Martha White

Modern reinforcement learning (RL) can be categorized into online and offline variants. As a pivotal aspect of both online and offline RL, current research on the Bellman equation revolves primarily around optimization techniques and…

Machine Learning · Computer Science 2023-12-14 Outongyi Lv , Bingxin Zhou

We study reinforcement learning in infinite-horizon discounted Markov decision processes with continuous state spaces, where data are generated online from a single trajectory under a Markovian behavior policy. To avoid maintaining an…

Machine Learning · Computer Science 2026-03-05 Shengbo Wang

Quantifying uncertainty about a policy's long-term performance is important to solve sequential decision-making tasks. We study the problem from a model-based Bayesian reinforcement learning perspective, where the goal is to learn the…

Machine Learning · Computer Science 2024-09-04 Carlos E. Luis , Alessandro G. Bottero , Julia Vinogradska , Felix Berkenkamp , Jan Peters

This paper develops an online inverse reinforcement learning algorithm aimed at efficiently recovering a reward function from ongoing observations of an agent's actions. To reduce the computation time and storage space in reward estimation,…

Robotics · Computer Science 2017-08-01 Kun Li , Joel W. Burdick

We study offline multitask reinforcement learning in settings where multiple tasks share a low-rank representation of their action-value functions. In this regime, a learner is provided with fixed datasets collected from several related…

Machine Learning · Computer Science 2026-04-28 Kausthubh Manda , Raghuram Bharadwaj Diddigi

State-action value functions (i.e., Q-values) are ubiquitous in reinforcement learning (RL), giving rise to popular algorithms such as SARSA and Q-learning. We propose a new notion of action value defined by a Gaussian smoothed version of…

Machine Learning · Computer Science 2018-07-26 Ofir Nachum , Mohammad Norouzi , George Tucker , Dale Schuurmans

Gradient-regularized value learning methods improve sample efficiency by leveraging learned models of transition dynamics and rewards to estimate return gradients. However, existing approaches, such as MAGE, struggle in stochastic or noisy…

Machine Learning · Computer Science 2026-03-04 Baptiste Debes , Tinne Tuytelaars

In offline reinforcement learning, in-sample learning methods have been widely used to prevent performance degradation caused by evaluating out-of-distribution actions from the dataset. Extreme Q-learning (XQL) employs a loss function based…

Machine Learning · Computer Science 2025-02-12 Motoki Omura , Takayuki Osa , Yusuke Mukuta , Tatsuya Harada

We show that the popular reinforcement learning (RL) strategy of estimating the state-action value (Q-function) by minimizing the mean squared Bellman error leads to a regression problem with confounding, the inputs and output noise being…

Machine Learning · Computer Science 2022-12-01 Yutian Chen , Liyuan Xu , Caglar Gulcehre , Tom Le Paine , Arthur Gretton , Nando de Freitas , Arnaud Doucet

Recent methods for imitation learning directly learn a $Q$-function using an implicit reward formulation rather than an explicit reward function. However, these methods generally require implicit reward regularization to improve stability…

Machine Learning · Computer Science 2023-03-02 Firas Al-Hafez , Davide Tateo , Oleg Arenz , Guoping Zhao , Jan Peters

The Mean Square Error (MSE) is commonly utilized to estimate the solution of the optimal value function in the vast majority of offline reinforcement learning (RL) models and has achieved outstanding performance. However, we find that its…

Machine Learning · Computer Science 2024-06-06 Yu Zhang , Rui Yu , Zhipeng Yao , Wenyuan Zhang , Jun Wang , Liming Zhang

Double Q-learning is a classical method for reducing overestimation bias, which is caused by taking maximum estimated values in the Bellman operation. Its variants in the deep Q-learning paradigm have shown great promise in producing…

Machine Learning · Computer Science 2022-01-17 Zhizhou Ren , Guangxiang Zhu , Hao Hu , Beining Han , Jianglun Chen , Chongjie Zhang

We propose a new reinforcement learning algorithm derived from a regularized linear-programming formulation of optimal control in MDPs. The method is closely related to the classic Relative Entropy Policy Search (REPS) algorithm of Peters…

Machine Learning · Computer Science 2021-03-01 Joan Bas-Serrano , Sebastian Curi , Andreas Krause , Gergely Neu

Model-free reinforcement learning algorithms, such as Q-learning, perform poorly in the early stages of learning in noisy environments, because much effort is spent unlearning biased estimates of the state-action value function. The bias…

Machine Learning · Computer Science 2018-02-01 Roy Fox , Ari Pakman , Naftali Tishby

Offline Reinforcement Learning (RL) struggles with distributional shifts, leading to the $Q$-value overestimation for out-of-distribution (OOD) actions. Existing methods address this issue by imposing constraints; however, they often become…

Machine Learning · Computer Science 2025-06-11 Qingmao Yao , Zhichao Lei , Tianyuan Chen , Ziyue Yuan , Xuefan Chen , Jianxiang Liu , Faguo Wu , Xiao Zhang

In reinforcement learning (RL), temporal difference (TD) errors are widely adopted for optimizing value and policy functions. However, since the TD error is defined by a bootstrap method, its computation tends to be noisy and destabilize…

Machine Learning · Computer Science 2026-04-03 Taisuke Kobayashi
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