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. 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 2.2 Accelerated rate for Bellman optimality opera We now present the accelerated convergence rate of Anc-VI for the Bellman optimality operator. Our analysis uses what we call the Bellman anti-optimality operator, define Anc-VI with the Bellman optimality operator exhibits the same accelerated convergence rate as Anc-VI with the Bellman consistency operator. As in Theorem 1, the rate of Theorem 2 also becomes O(1/k) when γ ≈ 1, while VI has a O(1)-rate. Proof outline of Theorem 2. The key technical challenge of the proof comes from the fact that the Bellman optimality operator is non-linear. Similar to the Bellman consistency operator case, we have This paper is available on arxiv under CC BY 4.0 DEED license. 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. Authors: 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. Abstract and 1 Introduction Abstract and 1 Introduction 1.1 Notations and preliminaries 1.1 Notations and preliminaries 1.2 Prior works 1.2 Prior works 2 Anchored Value Iteration 2 Anchored Value Iteration 2.1 Accelerated rate for Bellman consistency operator 2.1 Accelerated rate for Bellman consistency operator 2.2 Accelerated rate for Bellman optimality opera 2.2 Accelerated rate for Bellman optimality opera 3 Convergence when y=1 3 Convergence when y=1 4 Complexity lower bound 4 Complexity lower bound 5 Approximate Anchored Value Iteration 5 Approximate Anchored Value Iteration 6 Gauss–Seidel Anchored Value Iteration 6 Gauss–Seidel Anchored Value Iteration 7 Conclusion, Acknowledgments and Disclosure of Funding and References 7 Conclusion, Acknowledgments and Disclosure of Funding and References A Preliminaries A Preliminaries B Omitted proofs in Section 2 B Omitted proofs in Section 2 C Omitted proofs in Section 3 C Omitted proofs in Section 3 D Omitted proofs in Section 4 D Omitted proofs in Section 4 E Omitted proofs in Section 5 E Omitted proofs in Section 5 F Omitted proofs in Section 6 F Omitted proofs in Section 6 G Broader Impacts G Broader Impacts H Limitations H Limitations 2.2 Accelerated rate for Bellman optimality opera We now present the accelerated convergence rate of Anc-VI for the Bellman optimality operator. Our analysis uses what we call the Bellman anti-optimality operator, define Anc-VI with the Bellman optimality operator exhibits the same accelerated convergence rate as Anc-VI with the Bellman consistency operator. As in Theorem 1, the rate of Theorem 2 also becomes O(1/k) when γ ≈ 1, while VI has a O(1)-rate. Proof outline of Theorem 2. The key technical challenge of the proof comes from the fact that the Bellman optimality operator is non-linear. Similar to the Bellman consistency operator case, we have This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv

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