Online Learning for Unknown Partially Observable MDPs
This provides the first online RL algorithm with sub-linear regret for POMDPs, addressing a critical gap in learning optimal controllers under partial observability.
The paper tackles the problem of online learning for unknown partially observable Markov decision processes (POMDPs) by proposing a posterior sampling-based reinforcement learning algorithm, achieving a regret bound of O(log T) for finite parameter sets and O(T^{2/3}) for continuous sets.
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 a known observation model. We propose a natural posterior sampling-based reinforcement learning algorithm (PSRL-POMDP) and show that it achieves a regret bound of $O(\log T)$, where $T$ is the time horizon, when the parameter set is finite. In the general case (continuous parameter set), we show that the algorithm achieves $O (T^{2/3})$ regret under two technical assumptions. To the best of our knowledge, this is the first online RL algorithm for POMDPs and has sub-linear regret.