What Makes AI Work? A Breakdown of the Key Proofs

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

E Omitted proofs in Section 5

First, we prove following key lemma.

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

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

If k= 1,

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

Now, we prove the first rate in Theorem 6.

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

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

Now, we prove the second rate in Theorem 6.