On the Global Convergence of Fitted Q-Iteration with Two-layer Neural Network Parametrization

Mudit Gaur, Vaneet Aggarwal, Mridul Agarwal
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:11013-11049, 2023.

Abstract

Deep Q-learning based algorithms have been applied successfully in many decision making problems, while their theoretical foundations are not as well understood. In this paper, we study a Fitted Q-Iteration with two-layer ReLU neural network parameterization, and find the sample complexity guarantees for the algorithm. Our approach estimates the Q-function in each iteration using a convex optimization problem. We show that this approach achieves a sample complexity of $\tilde{\mathcal{O}}(1/\epsilon^{2})$, which is order-optimal. This result holds for a countable state-spaces and does not require any assumptions such as a linear or low rank structure on the MDP.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-gaur23a, title = {On the Global Convergence of Fitted Q-Iteration with Two-layer Neural Network Parametrization}, author = {Gaur, Mudit and Aggarwal, Vaneet and Agarwal, Mridul}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {11013--11049}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/gaur23a/gaur23a.pdf}, url = {https://proceedings.mlr.press/v202/gaur23a.html}, abstract = {Deep Q-learning based algorithms have been applied successfully in many decision making problems, while their theoretical foundations are not as well understood. In this paper, we study a Fitted Q-Iteration with two-layer ReLU neural network parameterization, and find the sample complexity guarantees for the algorithm. Our approach estimates the Q-function in each iteration using a convex optimization problem. We show that this approach achieves a sample complexity of $\tilde{\mathcal{O}}(1/\epsilon^{2})$, which is order-optimal. This result holds for a countable state-spaces and does not require any assumptions such as a linear or low rank structure on the MDP.} }
Endnote
%0 Conference Paper %T On the Global Convergence of Fitted Q-Iteration with Two-layer Neural Network Parametrization %A Mudit Gaur %A Vaneet Aggarwal %A Mridul Agarwal %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-gaur23a %I PMLR %P 11013--11049 %U https://proceedings.mlr.press/v202/gaur23a.html %V 202 %X Deep Q-learning based algorithms have been applied successfully in many decision making problems, while their theoretical foundations are not as well understood. In this paper, we study a Fitted Q-Iteration with two-layer ReLU neural network parameterization, and find the sample complexity guarantees for the algorithm. Our approach estimates the Q-function in each iteration using a convex optimization problem. We show that this approach achieves a sample complexity of $\tilde{\mathcal{O}}(1/\epsilon^{2})$, which is order-optimal. This result holds for a countable state-spaces and does not require any assumptions such as a linear or low rank structure on the MDP.
APA
Gaur, M., Aggarwal, V. & Agarwal, M.. (2023). On the Global Convergence of Fitted Q-Iteration with Two-layer Neural Network Parametrization. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:11013-11049 Available from https://proceedings.mlr.press/v202/gaur23a.html.

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