Online Sparse Reinforcement Learning

Botao Hao, Tor Lattimore, Csaba Szepesvari, Mengdi Wang
Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, PMLR 130:316-324, 2021.

Abstract

We investigate the hardness of online reinforcement learning in sparse linear Markov decision process (MDP), with a special focus on the high-dimensional regime where the ambient dimension is larger than the number of episodes. Our contribution is two-fold. First, we provide a lower bound showing that linear regret is generally unavoidable, even if there exists a policy that collects well-conditioned data. Second, we show that if the learner has oracle access to a policy that collects well-conditioned data, then a variant of Lasso fitted Q-iteration enjoys a regret of $O(N^{2/3})$ where $N$ is the number of episodes.

Cite this Paper

BibTeX
@InProceedings{pmlr-v130-hao21a, title = { Online Sparse Reinforcement Learning }, author = {Hao, Botao and Lattimore, Tor and Szepesvari, Csaba and Wang, Mengdi}, booktitle = {Proceedings of The 24th International Conference on Artificial Intelligence and Statistics}, pages = {316--324}, year = {2021}, editor = {Banerjee, Arindam and Fukumizu, Kenji}, volume = {130}, series = {Proceedings of Machine Learning Research}, month = {13--15 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v130/hao21a/hao21a.pdf}, url = {https://proceedings.mlr.press/v130/hao21a.html}, abstract = { We investigate the hardness of online reinforcement learning in sparse linear Markov decision process (MDP), with a special focus on the high-dimensional regime where the ambient dimension is larger than the number of episodes. Our contribution is two-fold. First, we provide a lower bound showing that linear regret is generally unavoidable, even if there exists a policy that collects well-conditioned data. Second, we show that if the learner has oracle access to a policy that collects well-conditioned data, then a variant of Lasso fitted Q-iteration enjoys a regret of $O(N^{2/3})$ where $N$ is the number of episodes. } }
Endnote
%0 Conference Paper %T Online Sparse Reinforcement Learning %A Botao Hao %A Tor Lattimore %A Csaba Szepesvari %A Mengdi Wang %B Proceedings of The 24th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2021 %E Arindam Banerjee %E Kenji Fukumizu %F pmlr-v130-hao21a %I PMLR %P 316--324 %U https://proceedings.mlr.press/v130/hao21a.html %V 130 %X We investigate the hardness of online reinforcement learning in sparse linear Markov decision process (MDP), with a special focus on the high-dimensional regime where the ambient dimension is larger than the number of episodes. Our contribution is two-fold. First, we provide a lower bound showing that linear regret is generally unavoidable, even if there exists a policy that collects well-conditioned data. Second, we show that if the learner has oracle access to a policy that collects well-conditioned data, then a variant of Lasso fitted Q-iteration enjoys a regret of $O(N^{2/3})$ where $N$ is the number of episodes.
APA
Hao, B., Lattimore, T., Szepesvari, C. & Wang, M.. (2021). Online Sparse Reinforcement Learning . Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 130:316-324 Available from https://proceedings.mlr.press/v130/hao21a.html.

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