  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.
