Adversarial Online Multi-Task Reinforcement Learning

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 M are well-separated under a notion of λ-separability, and show that this notion generalizes many task-separability notions from previous works. We prove a minimax lower bound of Omega(K√DSAH) on the regret of any learning algorithm and an instance-specific lower bound of Omega(fracKλ2) 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 tildeO(fracKλ2) sample complexity guarantee for the clustering phase and tildeO(√MK) regret guarantee for the learning phase, indicating that the dependency on K and frac1λ2 is tight.