What Makes AI Work? A Breakdown of the Key Proofs

:::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

First, we prove following key lemma.

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\ and let U¯ be the entire right hand side of inequality. Then, we have

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\ Now, we prove second inequality in Lemma 17 by induction.

\ If k= 1,

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\ and let U¯ be the entire right hand side of inequality. Then, we have

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\ Now, we prove the first rate in Theorem 6.

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\ Now, for the second rate in Theorem 6, we present following key lemma.

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\ let U¯ be the entire right hand side of inequality. Then, we have

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\ Now, we prove the second rate in Theorem 6.

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

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