Learning Infinite-horizon Average-reward MDPs with Linear Function Approximation

Chen-Yu Wei, Mehdi Jafarnia Jahromi, Haipeng Luo, Rahul Jain
Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, PMLR 130:3007-3015, 2021.

Abstract

We develop several new algorithms for learning Markov Decision Processes in an infinite-horizon average-reward setting with linear function approximation. Using the optimism principle and assuming that the MDP has a linear structure, we first propose a computationally inefficient algorithm with optimal O(\sqrt{T}) regret and another computationally efficient variant with O(T^{3/4}) regret, where T is the number of interactions. Next, taking inspiration from adversarial linear bandits, we develop yet another efficient algorithm with O(\sqrt{T}) regret under a different set of assumptions, improving the best existing result by Hao et al. (2020) with O(T^{2/3}) regret. Moreover, we draw a connection between this algorithm and the Natural Policy Gradient algorithm proposed by Kakade (2002), and show that our analysis improves the sample complexity bound recently given by Agarwal et al. (2020).

Cite this Paper

BibTeX
@InProceedings{pmlr-v130-wei21d, title = { Learning Infinite-horizon Average-reward MDPs with Linear Function Approximation }, author = {Wei, Chen-Yu and Jafarnia Jahromi, Mehdi and Luo, Haipeng and Jain, Rahul}, booktitle = {Proceedings of The 24th International Conference on Artificial Intelligence and Statistics}, pages = {3007--3015}, 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/wei21d/wei21d.pdf}, url = {https://proceedings.mlr.press/v130/wei21d.html}, abstract = { We develop several new algorithms for learning Markov Decision Processes in an infinite-horizon average-reward setting with linear function approximation. Using the optimism principle and assuming that the MDP has a linear structure, we first propose a computationally inefficient algorithm with optimal O(\sqrt{T}) regret and another computationally efficient variant with O(T^{3/4}) regret, where T is the number of interactions. Next, taking inspiration from adversarial linear bandits, we develop yet another efficient algorithm with O(\sqrt{T}) regret under a different set of assumptions, improving the best existing result by Hao et al. (2020) with O(T^{2/3}) regret. Moreover, we draw a connection between this algorithm and the Natural Policy Gradient algorithm proposed by Kakade (2002), and show that our analysis improves the sample complexity bound recently given by Agarwal et al. (2020). } }
Endnote
%0 Conference Paper %T Learning Infinite-horizon Average-reward MDPs with Linear Function Approximation %A Chen-Yu Wei %A Mehdi Jafarnia Jahromi %A Haipeng Luo %A Rahul Jain %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-wei21d %I PMLR %P 3007--3015 %U https://proceedings.mlr.press/v130/wei21d.html %V 130 %X We develop several new algorithms for learning Markov Decision Processes in an infinite-horizon average-reward setting with linear function approximation. Using the optimism principle and assuming that the MDP has a linear structure, we first propose a computationally inefficient algorithm with optimal O(\sqrt{T}) regret and another computationally efficient variant with O(T^{3/4}) regret, where T is the number of interactions. Next, taking inspiration from adversarial linear bandits, we develop yet another efficient algorithm with O(\sqrt{T}) regret under a different set of assumptions, improving the best existing result by Hao et al. (2020) with O(T^{2/3}) regret. Moreover, we draw a connection between this algorithm and the Natural Policy Gradient algorithm proposed by Kakade (2002), and show that our analysis improves the sample complexity bound recently given by Agarwal et al. (2020).
APA
Wei, C., Jafarnia Jahromi, M., Luo, H. & Jain, R.. (2021). Learning Infinite-horizon Average-reward MDPs with Linear Function Approximation . Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 130:3007-3015 Available from https://proceedings.mlr.press/v130/wei21d.html.

Related Material