Markov Decision Processes and Value Iteration in Reinforcement Learning

This section reviews key concepts in Markov Decision Processes (MDP) and reinforcement learning, covering notations, value iteration, and Bellman operators for optimal policy calculation.


This content originally appeared on HackerNoon and was authored by Anchoring

:::info Authors:

(1) Jongmin Lee, Department of Mathematical Science, Seoul National University;

(2) Ernest K. Ryu, Department of Mathematical Science, Seoul National University and Interdisciplinary Program in Artificial Intelligence, Seoul National University.

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Abstract and 1 Introduction

1.1 Notations and preliminaries

1.2 Prior works

2 Anchored Value Iteration

2.1 Accelerated rate for Bellman consistency operator

2.2 Accelerated rate for Bellman optimality opera

3 Convergence when y=1

4 Complexity lower bound

5 Approximate Anchored Value Iteration

6 Gauss–Seidel Anchored Value Iteration

7 Conclusion, Acknowledgments and Disclosure of Funding and References

A Preliminaries

B Omitted proofs in Section 2

C Omitted proofs in Section 3

D Omitted proofs in Section 4

E Omitted proofs in Section 5

F Omitted proofs in Section 6

G Broader Impacts

H Limitations

1.1 Notations and preliminaries

We quickly review basic definitions and concepts of Markov decision processes (MDP) and reinforcement learning (RL). For further details, refer to standard references such as [69, 81, 84].

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:::info This paper is available on arxiv under CC BY 4.0 DEED license.

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This content originally appeared on HackerNoon and was authored by Anchoring


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