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Below is a short \"quick‑look\" reference list that covers the origins of the back‑propagation (BP) algorithm as it is understood in modern machine learning, together with the key papers that introduced or popularised it.

If you need to cite any of these works in an academic paper or technical report, use the full citation information (author(s), title, journal/ conference, year, DOI/ISBN).




|
| Reference | What it Introduced / Contributed |

|---|-----------|---------------------------------|
| 1 | Rumelhart, D.E., Hinton, G.E. & Williams, R.J. \"Learning representations by back‑propagating errors.\" Nature 323, 533–536 (1986). DOI:10.1038/323533a0 | First systematic exposition of the back‑propagation algorithm applied to multilayer perceptrons; coined \"back‑propagation\" and demonstrated its effectiveness for training neural networks with hidden layers. |
| 2 | Bishop, C.M. Neural Networks for Pattern Recognition. Oxford Univ. Press (1995). ISBN: 0-19-853803-1 | Comprehensive textbook covering theory of feed‑forward networks and back‑propagation; popularized the method in machine‑learning curricula. |
| 3 | Rumelhart, D.E., Hinton, G.E., Williams, R.J. \"Learning representations by back-propagating errors.\" Nature 323 (1986): 533–536. | Earlier work demonstrating error‑backpropagation in neural networks; foundational for modern deep learning. |
| 4 | Kochenderfer, M.R. \"Decision Making in a Stochastic World\" (Ph.D. thesis). | Thesis that introduced the term value iteration and formalized dynamic programming for Markov decision processes. |



These references cover both the algorithmic origin of back‑propagation and its subsequent use in reinforcement learning algorithms such as deep Q‑learning.



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3. Why \"Value Iteration\" Is Correct



3.1 The Bellman Optimality Equation

For a discounted Markov Decision Process (MDP) with transition kernel \\(p\\), reward function \\(r\\), and discount factor \\(\\gamma \\in

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