Theoretical Hardness and Tractability of POMDPs in RL with Partial Online State Information

Partially observable Markov decision processes (POMDPs) have been widely applied in various real-world applications. However, existing theoretical results have shown that learning in POMDPs is intractable in the worst case, where the main challenge lies in the lack of latent state information. A key fundamental question here is: how much online state information (OSI) is sufficient to achieve tractability? In this paper, we establish a lower bound that reveals a surprising hardness result: unless we have full OSI, we need an exponentially scaling sample complexity to obtain an $\epsilon$-optimal policy solution for POMDPs. Nonetheless, inspired by the insights in our lower-bound design, we identify important tractable subclasses of POMDPs, even with only partial OSI. In particular, for two subclasses of POMDPs with partial OSI, we provide new algorithms that are proved to be near-optimal by establishing new regret upper and lower bounds. Both our algorithm design and regret analysis involve non-trivial developments for joint OSI query and action control.