  Solving Partially Observable Markov Decision Processes (POMDPs) is hard.
Learning optimal controllers for POMDPs when the model is unknown is harder.
Online learning of optimal controllers for unknown POMDPs, which requires
efficient learning using regret-minimizing algorithms that effectively tradeoff
exploration and exploitation, is even harder, and no solution exists currently.
In this paper, we consider infinite-horizon average-cost POMDPs with unknown
transition model, though known observation model. We propose a natural
posterior sampling-based reinforcement learning algorithm (POMDP-PSRL) and show
that it achieves $O(T^{2/3})$ regret where $T$ is the time horizon. To the best
of our knowledge, this is the first online RL algorithm for POMDPs and has
sub-linear regret.
