Simple statistical gradient-following algorithms for connectionist reinforcement learning
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The REINFORCE algorithm is a policy gradient method that adjusts parameters to favor actions that yield higher rewards and improve segmentation.
“The agent's policy is updated using the REINFORCE algorithm [20], a policy gradient method that adjusts its parameters to favor actions that yield higher rewards and improve segmentation.”
From Beyond Manual Annotation: A Human-AI Collaborative Framework for Medical Image Segmentation Using Only "Better or Worse" Expert Feedback (2025) · cites this paper as [20]
Section 4 defines REINFORCE as a parameter-update algorithm and shows that its average update follows a direction of increasing expected reward. The paper does not establish that REINFORCE improves segmentation; that is a claim about the citing paper’s application, not a result shown by this source. (LLM, conf=0.88)
Experimental — accuracy not yet measuredSuch methods commonly use online policy optimization algorithms such as PPO, GRPO, REINFORCE, and DAPO.
“These methods often employ online policy optimization algorithms, including Proximal Policy Optimization (PPO) (Schulman et al., 2017), Group Relative Policy Optimization (GRPO) (Shao et al., 2024a), REINFORCE (Williams, 1992), and Decoupled Clip and Dynamic Sampling Policy Optimization (DAPO) (Yu et al., 2025).”
From Critique-GRPO: Advancing LLM Reasoning with Natural Language and Numerical Feedback (2025) · cites this paper as Williams, 1992
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Research works printed but not linked: 22
- Barto, A.G. & Anandan, P. (1985). Pattern recognizing stochastic learning automata. IEEE Transactions on Systems, Man, and Cybernetics, 15, 360-374.
- Barto, A.G. & Anderson, C.W. (1985). Structural learning in connectionist systems. Proceedings of the Seventh Annual Conference of the Cognitive Science Society, (pp. 43-53).
- Barto, A.G., Sutton, R.S., & Anderson, C.W. (1983). Neuronlike elements that can solve difficult learning con- trol problems. IEEE Transactions on Systems, Man, and Cybernetics, 13, 835-846.
- Barto, A.G., & Jordan, M.I. (1987). Gradient following without back-propagation in layered networks. Proceedings of the First Annual International Conference on Neural Networks, Vol. II (pp. 629-636). San Diego, CA.
- Barto, A.G., Sutton, R.S., &Watkins, C.J.C.H. (1990). Learning and sequential decision making. In: M. Gabriel & J.W. Moore (Eds.), Learning and computational neuroscience: Foundations of adaptive networks. Cambridge, MA: MIT Press.
- Dayan, P. (1990). Reinforcement comparison. In D.S. Touretzky, J.L. Elman, T.J. Sejnowski, & G.E. Hinton (Eds.), Proceedings of the 1990 Connectionist Models Summer School (pp. 45-51). San Mateo, CA: Morgan Kaufmann.
- Hinton, G.E. & Sejnowski, T.J. (1986). Learning and relearning in Boltzmann machines. In: D.E. Rumelhart & J.L. McClelland, (Eds.), Parallel distributed processing: Explorations in the microstructure of cognition. Vol. 1: Foundations. Cambridge, MA: MIT Press.
- Jordan, M.I. & Rumelhart, D.E. (1990). Forward models: supervised learning with a distal teacher. (Occasional Paper -40). Cambridge, MA: Massachusetts Institute of Technology, Center for Cognitive Science.
- leCun, Y. (1985). Une procedure d'apprentissage pour resau a sequil assymetrique [A learning procedure for asymmetric threshold networks]. Proceedings of Cognitiva, 85, 599-604.
- Munro, P. (1987). A dual back-propagation scheme for scalar reward learning. Proceedings of the Ninth Annual Conference of the Cognitive Science Society (pp. 165-176). Seattle, WA.
- Narendra, K.S. & Thathatchar, M.A.L. (1989). Learning Automata: An introduction. Englewood Cliffs, NJ: Prentice Hall.
- Narendra, K.S. & Wheeler, R.M., Jr. (1983). An N-player sequential stochastic game with identical payoffs. IEEE Transactions on Systems, Man, and Cybernetics, 13, 1154-1158.
- Parker, D.B. (1985). Learning-logic. (Technical Report TR-47). Cambridge, MA: Massachusetts Institute of Tech- nology, Center for Computational Research in Economics and Management Science.
- Rohatgi, V.K. (1976) An introduction to probability theory and mathematical statistics. New York: Wiley.
- Rumelhart, D.E., Hinton, G.E., & Williams, R.J. (1986). Learning internal representations by error propaga- tion. In: D.E. Rumelhart & J.L. McClelland, (Eds.), Parallel distributed processing: Explorations in the micro- structure of cognition. Vol. 1: Foundations. Cambridge: MIT Press.
- Sutton, R.S. (1984). Temporal credit assignment in reinforcement learning. Ph.D. Dissertation, Dept. of Com- puter and Information Science, University of Massachusetts, Amherst, MA.
- Thathatchar, M.A.L. & Sastry, P.S. (1985). A new approach to the design of reinforcement schemes for learning automata. IEEE Transactions on Systems, Man, and Cybernetics, 15, 168-175.
- Wheeler, R.M., Jr. & Narendra K.S. (1986). Decentralized learning in finite Markov chains. IEEE Transactions on Automatic Control, 31, 519-526.
- Watkins, C.J.C.H. (1989). Learning from delayed rewards. Ph.D. Dissertation, Cambridge University, Cambridge, England.
- Werbos, P.J. (1974). Beyond regression: new tools for prediction and analysis in the behavioral sciences. Ph.D. Dissertation, Harvard University, Cambridge, MA.
- Williams, R.J. (1987b). A class of gradient-estimating algorithms for reinforcement learning in neural networks. Proceedings of the First Annual International Conference on Neural Networks, Vol. II (pp. 601-608). San Diego, CA.
- Williams, R.J. (1988a). On the use of backpropagation in associative reinforcement learning. Proceedings of the Second Annual International Conference on Neural Networks, Vol. I (pp. 263-270). San Diego, CA.
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- Authors
- Williams, R. J.
- Affiliations
- Northeastern University (US)
- Corresponding author
- Williams, Ronald J.
- Venue
- Machine Learning
- Published
- 1992-05
- Volume
- 8
- Issue
- 3-4
- Pages
- 229-256
- ISSN
- 0885-6125 (ISSN-L)
- 1573-0565
- OpenAlex
- W4241811150
- Cited by
- 817
- References
- 0
- Citations by year
- 2026: 296 · 2025: 264 · 2024: 83 · 2023: 30 · 2022: 29 · 2021: 34 · 2020: 26 · 2019: 29 · 2018: 8 · 2017: 8 · 2015: 2 · 2012: 1
- FWCI
- 0.45
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- Locations
- Machine Learning (publishedVersion)
- Funders
- National Science Foundation (8921275)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Reinforcement Learning in Robotics
- Physical Sciences › Computer Science › Artificial Intelligence › Neural Networks and Applications
- Physical Sciences › Computer Science › Artificial Intelligence › Machine Learning and Algorithms
- Keywords
- REINFORCE algorithm, delayed reinforcement, backpropagation, weight adjustment, asymptotic behavior
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