Adversarial Online Multi-Task Reinforcement Learning

Quan Nguyen, Nishant Mehta
Proceedings of The 34th International Conference on Algorithmic Learning Theory, PMLR 201:1124-1165, 2023.

Abstract

We consider the adversarial online multi-task reinforcement learning setting, where in each of $K$ episodes the learner is given an unknown task taken from a finite set of $M$ unknown finite-horizon MDP models. The learner’s objective is to minimize its regret with respect to the optimal policy for each task. We assume the MDPs in $\mathcal{M}$ are well-separated under a notion of $\lambda$-separability, and show that this notion generalizes many task-separability notions from previous works. We prove a minimax lower bound of $\Omega(K\sqrt{DSAH})$ on the regret of any learning algorithm and an instance-specific lower bound of $\Omega(\frac{K}{\lambda^2})$ in sample complexity for a class of \emph{uniformly good} cluster-then-learn algorithms. We use a novel construction called $\emph{2-JAO MDP}$ for proving the instance-specific lower bound. The lower bounds are complemented with a polynomial time algorithm that obtains $\tilde{O}(\frac{K}{\lambda^2})$ sample complexity guarantee for the clustering phase and $\tilde{O}(\sqrt{MK})$ regret guarantee for the learning phase, indicating that the dependency on $K$ and $\frac{1}{\lambda^2}$ is tight.

Cite this Paper

BibTeX
@InProceedings{pmlr-v201-nguyen23a, title = {Adversarial Online Multi-Task Reinforcement Learning}, author = {Nguyen, Quan and Mehta, Nishant}, booktitle = {Proceedings of The 34th International Conference on Algorithmic Learning Theory}, pages = {1124--1165}, year = {2023}, editor = {Agrawal, Shipra and Orabona, Francesco}, volume = {201}, series = {Proceedings of Machine Learning Research}, month = {20 Feb--23 Feb}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v201/nguyen23a/nguyen23a.pdf}, url = {https://proceedings.mlr.press/v201/nguyen23a.html}, abstract = { We consider the adversarial online multi-task reinforcement learning setting, where in each of $K$ episodes the learner is given an unknown task taken from a finite set of $M$ unknown finite-horizon MDP models. The learner’s objective is to minimize its regret with respect to the optimal policy for each task. We assume the MDPs in $\mathcal{M}$ are well-separated under a notion of $\lambda$-separability, and show that this notion generalizes many task-separability notions from previous works. We prove a minimax lower bound of $\Omega(K\sqrt{DSAH})$ on the regret of any learning algorithm and an instance-specific lower bound of $\Omega(\frac{K}{\lambda^2})$ in sample complexity for a class of \emph{uniformly good} cluster-then-learn algorithms. We use a novel construction called $\emph{2-JAO MDP}$ for proving the instance-specific lower bound. The lower bounds are complemented with a polynomial time algorithm that obtains $\tilde{O}(\frac{K}{\lambda^2})$ sample complexity guarantee for the clustering phase and $\tilde{O}(\sqrt{MK})$ regret guarantee for the learning phase, indicating that the dependency on $K$ and $\frac{1}{\lambda^2}$ is tight.} }
Endnote
%0 Conference Paper %T Adversarial Online Multi-Task Reinforcement Learning %A Quan Nguyen %A Nishant Mehta %B Proceedings of The 34th International Conference on Algorithmic Learning Theory %C Proceedings of Machine Learning Research %D 2023 %E Shipra Agrawal %E Francesco Orabona %F pmlr-v201-nguyen23a %I PMLR %P 1124--1165 %U https://proceedings.mlr.press/v201/nguyen23a.html %V 201 %X We consider the adversarial online multi-task reinforcement learning setting, where in each of $K$ episodes the learner is given an unknown task taken from a finite set of $M$ unknown finite-horizon MDP models. The learner’s objective is to minimize its regret with respect to the optimal policy for each task. We assume the MDPs in $\mathcal{M}$ are well-separated under a notion of $\lambda$-separability, and show that this notion generalizes many task-separability notions from previous works. We prove a minimax lower bound of $\Omega(K\sqrt{DSAH})$ on the regret of any learning algorithm and an instance-specific lower bound of $\Omega(\frac{K}{\lambda^2})$ in sample complexity for a class of \emph{uniformly good} cluster-then-learn algorithms. We use a novel construction called $\emph{2-JAO MDP}$ for proving the instance-specific lower bound. The lower bounds are complemented with a polynomial time algorithm that obtains $\tilde{O}(\frac{K}{\lambda^2})$ sample complexity guarantee for the clustering phase and $\tilde{O}(\sqrt{MK})$ regret guarantee for the learning phase, indicating that the dependency on $K$ and $\frac{1}{\lambda^2}$ is tight.
APA
Nguyen, Q. & Mehta, N.. (2023). Adversarial Online Multi-Task Reinforcement Learning. Proceedings of The 34th International Conference on Algorithmic Learning Theory, in Proceedings of Machine Learning Research 201:1124-1165 Available from https://proceedings.mlr.press/v201/nguyen23a.html.

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