Adversarial Online Multi-Task Reinforcement Learning

• URL: http://arxiv.org/abs/2301.04268v1
• Date: Wed, 11 Jan 2023 02:18:26 GMT
• Title: Adversarial Online Multi-Task Reinforcement Learning
• Authors: Quan Nguyen and Nishant A. Mehta
• Abstract summary: We consider the adversarial online multi-task reinforcement learning setting. 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 generalize its regret with respect to the optimal policy for each task.
• Score: 12.421997449847153
• License: http://creativecommons.org/licenses/by/4.0/
• 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 uniformly-good cluster-then-learn algorithms. We use a novel construction called 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.

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