PAC Reinforcement Learning with Rich Observations

We propose and study a new tractable model for reinforcement learning with rich observations called Contextual-MDPs, generalizing contextual bandits to sequential decision making. These models require an agent to take actions based on observations (features) with the goal of achieving long-term performance competitive with a large set of policies. To avoid barriers to sample-efficient learning associated with large observation spaces and general POMDPs, Contextual-MDPs can be summarized by a small number of hidden states and long-term rewards are predictable by a reactive function class. In this setting, we design a new reinforcement learning algorithm that engages in global exploration and analyze its sample complexity. We prove that the algorithm learns near optimal behavior after a number of episodes that is polynomial in all relevant parameters, logarithmic in the number of policies, and independent of the size of the observation space. This represents an exponential improvement over all existing alternative approaches and provides theoretical justification for reinforcement learning with function approximation.