We study episodic reinforcement learning in Markov decision processes when the agent receives additional feedback per step in the form of several transition observations. Such additional observations are available in a range of tasks through extended sensors or prior knowledge about the environment (e.g., when certain actions yield similar outcome). We formalize this setting using a feedback graph over state-action pairs and show that model-based algorithms can leverage the additional feedback for more sample-efficient learning. We give a regret bound that, ignoring logarithmic factors and lower-order terms, depends only on the size of the maximum acyclic subgraph of the feedback graph, in contrast with a polynomial dependency on the number of states and actions in the absence of a feedback graph. Finally, we highlight challenges when leveraging a small dominating set of the feedback graph as compared to the bandit setting and propose a new algorithm that can use knowledge of such a dominating set for more sample-efficient learning of a near-optimal policy.
Download