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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1.1 Notations and preliminaries
2.1 Accelerated rate for Bellman consistency operator
2.2 Accelerated rate for Bellman optimality opera
5 Approximate Anchored Value Iteration
6 Gauss–Seidel Anchored Value Iteration
7 Conclusion, Acknowledgments and Disclosure of Funding and References
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
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\ 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
\
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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
Anchoring | Sciencx (2025-01-14T22:56:26+00:00) How Anc-VI Helps AI Learn Faster with Optimality Operators. Retrieved from https://www.scien.cx/2025/01/14/how-anc-vi-helps-ai-learn-faster-with-optimality-operators/
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