An Improved Finite-time Analysis of Temporal Difference Learning with Deep Neural Networks

Zhifa Ke, Zaiwen Wen, Junyu Zhang
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:23407-23429, 2024.

Abstract

Temporal difference (TD) learning algorithms with neural network function parameterization have well-established empirical success in many practical large-scale reinforcement learning tasks. However, theoretical understanding of these algorithms remains challenging due to the nonlinearity of the action-value approximation. In this paper, we develop an improved non-asymptotic analysis of the neural TD method with a general $L$-layer neural network. New proof techniques are developed and an improved new $\tilde{\mathcal{O}}(\epsilon^{-1})$ sample complexity is derived. To our best knowledge, this is the first finite-time analysis of neural TD that achieves an $\tilde{\mathcal{O}}(\epsilon^{-1})$ complexity under the Markovian sampling, as opposed to the best known $\tilde{\mathcal{O}}(\epsilon^{-2})$ complexity in the existing literature.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-ke24b, title = {An Improved Finite-time Analysis of Temporal Difference Learning with Deep Neural Networks}, author = {Ke, Zhifa and Wen, Zaiwen and Zhang, Junyu}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {23407--23429}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/ke24b/ke24b.pdf}, url = {https://proceedings.mlr.press/v235/ke24b.html}, abstract = {Temporal difference (TD) learning algorithms with neural network function parameterization have well-established empirical success in many practical large-scale reinforcement learning tasks. However, theoretical understanding of these algorithms remains challenging due to the nonlinearity of the action-value approximation. In this paper, we develop an improved non-asymptotic analysis of the neural TD method with a general $L$-layer neural network. New proof techniques are developed and an improved new $\tilde{\mathcal{O}}(\epsilon^{-1})$ sample complexity is derived. To our best knowledge, this is the first finite-time analysis of neural TD that achieves an $\tilde{\mathcal{O}}(\epsilon^{-1})$ complexity under the Markovian sampling, as opposed to the best known $\tilde{\mathcal{O}}(\epsilon^{-2})$ complexity in the existing literature.} }
Endnote
%0 Conference Paper %T An Improved Finite-time Analysis of Temporal Difference Learning with Deep Neural Networks %A Zhifa Ke %A Zaiwen Wen %A Junyu Zhang %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-ke24b %I PMLR %P 23407--23429 %U https://proceedings.mlr.press/v235/ke24b.html %V 235 %X Temporal difference (TD) learning algorithms with neural network function parameterization have well-established empirical success in many practical large-scale reinforcement learning tasks. However, theoretical understanding of these algorithms remains challenging due to the nonlinearity of the action-value approximation. In this paper, we develop an improved non-asymptotic analysis of the neural TD method with a general $L$-layer neural network. New proof techniques are developed and an improved new $\tilde{\mathcal{O}}(\epsilon^{-1})$ sample complexity is derived. To our best knowledge, this is the first finite-time analysis of neural TD that achieves an $\tilde{\mathcal{O}}(\epsilon^{-1})$ complexity under the Markovian sampling, as opposed to the best known $\tilde{\mathcal{O}}(\epsilon^{-2})$ complexity in the existing literature.
APA
Ke, Z., Wen, Z. & Zhang, J.. (2024). An Improved Finite-time Analysis of Temporal Difference Learning with Deep Neural Networks. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:23407-23429 Available from https://proceedings.mlr.press/v235/ke24b.html.

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