No-regret Exploration in Contextual Reinforcement Learning

We consider the recently proposed reinforcement learning (RL) framework of Contextual Markov Decision Processes (CMDP), where the agent interacts with a (potentially adversarial) sequence of episodic tabular MDPs. In addition, a context vector determining the MDP parameters is available to the agent at the start of each episode, thereby allowing it to learn a context-dependent near-optimal policy. In this paper, we propose a no-regret online RL algorithm in the setting where the MDP parameters are obtained from the context using generalized linear mappings (GLMs). We propose and analyze optimistic and randomized exploration methods which make (time and space) efficient online updates. The GLM based model subsumes previous work in this area and also improves previous known bounds in the special case where the contextual mapping is linear. In addition, we demonstrate a generic template to derive confidence sets using an online learning oracle and give a lower bound for the setting.