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Reinforcement Learning: An Introduction
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“Actor-Critic methods are a widely used class of reinforcement learning (RL) algorithms that integrate both policy-based and value-based approaches [80,81].”
From Adaptive Information Modulation: Designing Governance Mechanisms for Multi-Agent Artificial Intelligence Systems (2026) · cites this paper as [80]
In the citing paper
“Such attributions of causality are a precondition for learning,2”
From Two prefrontal-subcortical circuits estimate controllability and reflect its impact on learning (2026) · cites this paper as [3]
In the citing paper
“Another distinguishing aspect is that, in this framework, actions are triggered by goals through prediction errors, whereas in most reinforcement learning schemes, responses are triggered by stimuli via associative links – and prediction errors have only a role in learning (e.g., using Temporal Difference learning) (Sutton and Barto, 1998).”
From Active Inference, homeostatic regulation and adaptive behavioural control (2015) · cites this paper as Sutton and Barto, 1998
In the citing paper
“and interpreted in the framework of reinforcement learning (RL) theory4-5.”
From A reservoir of time constants for memory traces in cortical neurons (2011) · cites this paper as [5]
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Opportunities and Risks of LLMs for Scalable Deliberation with Polis
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“…routing is rooted in the fields of Active Learning (Cohn et al., 1996), also known as Sequential Design of Experiment in statistics, Bayesian Optimisation using Gaussian Processes (Rasmussen, 2006), Exploration/Exploitation in Reinforcement Learning and Bandits Algorithms Sutton and Barto (1998).”
MethodMobile-kube: mobility-aware and energy-efficient service orchestration on kubernetes edge servers
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BackgroundUsing dialogue acts to learn better repair strategies for spoken dialogue systems
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Automated Design of Agentic Systems
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“One could also include more classic approaches to balance exploration and exploitation (Sutton & Barto, 2018; Liu et al., 2024).”
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“MDP formulates the interaction between an actor and the environment [27].”
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“Reinforcement learning (RL), a subfield of machine learning, is a powerful approach that enables an agent to learn how to make optimal decisions automatically [135].”
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“To obtain single-trial estimates of participants' reward expectations and PEs, we fitted different reinforcement learning (RL) models to each participant's choice sequence and reinforcement history (Sutton and Barto 2018; Watkins and Dayan 1992).”
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“RL environments also induce feedback effects (Sutton & Barto, 2018).”
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Wang, P., Viberg, O., Law, E. L.-C., & Greiff, S. (2026) · Educational Psychology Review · doi:10.1007/s10648-026-10202-y · Cited by 3
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Two prefrontal-subcortical circuits estimate controllability and reflect its impact on learning
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“Grid world environments have a long history in RL research Sutton & Barto (2018), as they offer a number of attractive properties.”
BackgroundA Study of Global and Episodic Bonuses for Exploration in Contextual MDPs
Henaff, M., Jiang, M., & Raileanu, R. (2023) · arXiv · doi:10.48550/arxiv.2306.03236 · Cited by 1
“A large body of research has studied this problem within the Markov Decision Process (MDP) framework (Sutton & Barto, 2018), both from a theoretical standpoint (Kearns & Singh, 2002; Brafman & Tennenholtz, 2002; Agarwal et al., 2020) and an empirical one.”
BackgroundNested Learning: The Illusion of Deep Learning Architectures
Behrouz, A., Razaviyayn, M., Zhong, P., & Mirrokni, V. (2025) · arXiv · doi:10.48550/arxiv.2512.24695 · Cited by 37
Reward magnitude determines reinforcement learning efficiency
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Calibrating Conservatism for Scalable Oversight
Overman, W., & Bayati, M. (2026) · arXiv · doi:10.48550/arxiv.2605.28807
“We model interaction with the environment as a controlled Markov process (cMP), a standard Markov decision process without a fixed reward function (Sutton & Barto, 2018).”
A Perspective on Open Challenges in Deformable Object Manipulation
McKennaa, R. P., & Oyekan, J. (2026) · arXiv · doi:10.48550/arxiv.2602.22998 · Cited by 1
Kuo, P.-C., Hou, H., Dabney, W., & Walker, E. Y. (2025) · arXiv
“This issue is known in reinforcement learning (RL) as partial observability [1, 2, 3], and is a major challenge in the deployment of real-world RL systems [4].”
InfluentialHiveMind: Contribution-Guided Online Prompt Optimization of LLM Multi-Agent Systems
Xia, Y., Wang, T., Zhang, S., Weng, Z., Cao, B., & Liew, S. C. (2025) · arXiv · doi:10.48550/arxiv.2512.06432
“The problem of fairly attributing a collective outcome to individual contributors is a central theme in both reinforcement learning (Sutton and Barto 2018) and cooperative game theory.”
MAPLE-Guard: Memory-Aware Link Enforcement Against Memory-Link Poisoning in Multi-Agent Systems
Xiong, W., Zhou, Y., Wang, J., Gu, S., Tang, B., Li, Z., Xiong, F., Wen, Y., & Wen, M. (2026) · arXiv · doi:10.48550/arxiv.2608.00426 · Cited by 2
“In addition, a parallel line treats memory value as a learnable quantity: reinforcement-learning memory managers score which items are worth keeping and reusing [39, 46, 58], which is the substrate our guard governs.”
MEM1: Learning to Synergize Memory and Reasoning for Efficient Long-Horizon Agents
Zhou, Z., Qu, A., Wu, Z., Kim, S., Prakash, A., Rus, D., Zhao, J., Low, B. K. H., & Liang, P. P. (2025) · arXiv · doi:10.48550/arxiv.2506.15841 · Cited by 218
“We train this behavior end-to-end with reinforcement learning (RL) [48, 71], optimizing for task success via verifiable rewards [43].”
Leveraging Sequentiality in Reinforcement Learning from a Single Demonstration
Chenu, A., Serris, O., Sigaud, O., & Perrin-Gilbert, N. (2022) · arXiv · doi:10.48550/arxiv.2211.04786
“A discount factor γ describes the importance of long-term rewards in this sequence of interactions [11].”
Wang, W., Piękos, P., Nanbo, L., Laakom, F., Chen, Y., Ostaszewski, M., Zhuge, M., & Schmidhuber, J. (2025) · arXiv · doi:10.48550/arxiv.2510.21614 · Cited by 40
Reflect-RL: Two-Player Online RL Fine-Tuning for LMs
Zhou, R., Du, S. S., & Li, B. (2024) · arXiv · doi:10.48550/arxiv.2402.12621
Serevan, B., & Kuşakçı, A. O. (2026) · International Journal of Lean Six Sigma · doi:10.1108/ijlss-02-2026-0094
Hulse, B. K., Haberkern, H., Franconville, R., Turner-Evans, D. B., Takemura, S., Wolff, T., Noorman, M., Dreher, M., Dan, C., Parekh, R., et al. (2020) · doi:10.1101/2020.12.08.413955 · Cited by 392
TTRL: Test-Time Reinforcement Learning
Zuo, Y., Zhang, K., Sheng, L., Qu, S., Cui, G., Zhu, X., Li, H., Zhang, Y., Long, X., Hua, E., et al. (2025) · arXiv · Cited by 7
DORA Explorer: Improving the Exploration Ability of LLMs Without Training
Gurjar, P., Ishmam, M. F., & Marino, K. (2026) · arXiv · doi:10.48550/arxiv.2604.17244
Metadata
- Authors
- Sutton, R. S., & Barto, A. G.
- Affiliations
- MIT Press
- ORCID
- Sutton, R.S.
- Venue
- IEEE Transactions on Neural Networks
- Published
- 1998-09
- Volume
- 9
- Issue
- 5
- Pages
- 1054-1054
- ISSN
- 1045-9227 (ISSN-L)
- 1941-0093
- OpenAlex
- W4214717370
- Cited by
- 27,225
- References
- 0
- Citations by year
- 2026: 818 · 2025: 2403 · 2024: 2277 · 2023: 2382 · 2022: 2316 · 2021: 2022 · 2020: 1875 · 2019: 1731 · 2018: 1444 · 2017: 1058 · 2016: 852 · 2015: 782 · 2014: 892 · 2013: 817 · 2012: 816
- FWCI
- 95.54
- Type
- journal article
- Language
- en
- Open access
- closed
- Licence
- Locations
- IEEE Transactions on Neural Networks (publishedVersion)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Reinforcement Learning in Robotics
- Physical Sciences › Computer Science › Artificial Intelligence › Machine Learning and Algorithms
- Social Sciences › Decision Sciences › Management Science and Operations Research › Advanced Bandit Algorithms Research
- Keywords
- reinforcement learning, learning from interaction, optimal control, Markov decision process, policy optimization
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Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
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