Provably Efficient Exploration in Quantum Reinforcement Learning with Logarithmic Worst-Case Regret

Han Zhong, Jiachen Hu, Yecheng Xue, Tongyang Li, Liwei Wang
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:61681-61707, 2024.

Abstract

While quantum reinforcement learning (RL) has attracted a surge of attention recently, its theoretical understanding is limited. In particular, it remains elusive how to design provably efficient quantum RL algorithms that can address the exploration-exploitation trade-off. To this end, we propose a novel UCRL-style algorithm that takes advantage of quantum computing for tabular Markov decision processes (MDPs) with $S$ states, $A$ actions, and horizon $H$, and establish an $\mathcal{O}(\mathrm{poly}(S, A, H, \log T))$ worst-case regret for it, where $T$ is the number of episodes. Furthermore, we extend our results to quantum RL with linear function approximation, which is capable of handling problems with large state spaces. Specifically, we develop a quantum algorithm based on value target regression (VTR) for linear mixture MDPs with $d$-dimensional linear representation and prove that it enjoys $\mathcal{O}(\mathrm{poly}(d, H, \log T))$ regret. Our algorithms are variants of UCRL/UCRL-VTR algorithms in classical RL, which also leverage a novel combination of lazy updating mechanisms and quantum estimation subroutines. This is the key to breaking the $\Omega(\sqrt{T})$-regret barrier in classical RL. To the best of our knowledge, this is the first work studying the online exploration in quantum RL with provable logarithmic worst-case regret.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-zhong24b, title = {Provably Efficient Exploration in Quantum Reinforcement Learning with Logarithmic Worst-Case Regret}, author = {Zhong, Han and Hu, Jiachen and Xue, Yecheng and Li, Tongyang and Wang, Liwei}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {61681--61707}, 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/zhong24b/zhong24b.pdf}, url = {https://proceedings.mlr.press/v235/zhong24b.html}, abstract = {While quantum reinforcement learning (RL) has attracted a surge of attention recently, its theoretical understanding is limited. In particular, it remains elusive how to design provably efficient quantum RL algorithms that can address the exploration-exploitation trade-off. To this end, we propose a novel UCRL-style algorithm that takes advantage of quantum computing for tabular Markov decision processes (MDPs) with $S$ states, $A$ actions, and horizon $H$, and establish an $\mathcal{O}(\mathrm{poly}(S, A, H, \log T))$ worst-case regret for it, where $T$ is the number of episodes. Furthermore, we extend our results to quantum RL with linear function approximation, which is capable of handling problems with large state spaces. Specifically, we develop a quantum algorithm based on value target regression (VTR) for linear mixture MDPs with $d$-dimensional linear representation and prove that it enjoys $\mathcal{O}(\mathrm{poly}(d, H, \log T))$ regret. Our algorithms are variants of UCRL/UCRL-VTR algorithms in classical RL, which also leverage a novel combination of lazy updating mechanisms and quantum estimation subroutines. This is the key to breaking the $\Omega(\sqrt{T})$-regret barrier in classical RL. To the best of our knowledge, this is the first work studying the online exploration in quantum RL with provable logarithmic worst-case regret.} }
Endnote
%0 Conference Paper %T Provably Efficient Exploration in Quantum Reinforcement Learning with Logarithmic Worst-Case Regret %A Han Zhong %A Jiachen Hu %A Yecheng Xue %A Tongyang Li %A Liwei Wang %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-zhong24b %I PMLR %P 61681--61707 %U https://proceedings.mlr.press/v235/zhong24b.html %V 235 %X While quantum reinforcement learning (RL) has attracted a surge of attention recently, its theoretical understanding is limited. In particular, it remains elusive how to design provably efficient quantum RL algorithms that can address the exploration-exploitation trade-off. To this end, we propose a novel UCRL-style algorithm that takes advantage of quantum computing for tabular Markov decision processes (MDPs) with $S$ states, $A$ actions, and horizon $H$, and establish an $\mathcal{O}(\mathrm{poly}(S, A, H, \log T))$ worst-case regret for it, where $T$ is the number of episodes. Furthermore, we extend our results to quantum RL with linear function approximation, which is capable of handling problems with large state spaces. Specifically, we develop a quantum algorithm based on value target regression (VTR) for linear mixture MDPs with $d$-dimensional linear representation and prove that it enjoys $\mathcal{O}(\mathrm{poly}(d, H, \log T))$ regret. Our algorithms are variants of UCRL/UCRL-VTR algorithms in classical RL, which also leverage a novel combination of lazy updating mechanisms and quantum estimation subroutines. This is the key to breaking the $\Omega(\sqrt{T})$-regret barrier in classical RL. To the best of our knowledge, this is the first work studying the online exploration in quantum RL with provable logarithmic worst-case regret.
APA
Zhong, H., Hu, J., Xue, Y., Li, T. & Wang, L.. (2024). Provably Efficient Exploration in Quantum Reinforcement Learning with Logarithmic Worst-Case Regret. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:61681-61707 Available from https://proceedings.mlr.press/v235/zhong24b.html.

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