Sample-Efficient Learning of POMDPs with Multiple Observations In
  Hindsight
Jiacheng Guo Minshuo Chen Huan Wang Caiming Xiong Mengdi Wang Yu Bai
This paper studies the sample-efficiency of learning in Partially Observable
Markov Decision Processes (POMDPs), a challenging problem in reinforcement
learning that is known to be exponentially hard in the worst-case. Motivated by
real-world settings such as loading in game playing, we propose an enhanced
feedback model called ``multiple observations in hindsight'', where after each
episode of interaction with the POMDP, the learner may collect multiple
additional observations emitted from the encountered latent states, but may not
observe the latent states themselves. We show that sample-efficient learning
under this feedback model is possible for two new subclasses of POMDPs:
\emph{multi-observation revealing POMDPs} and \emph{distinguishable POMDPs}.
Both subclasses generalize and substantially relax \emph{revealing POMDPs} -- a
widely studied subclass for which sample-efficient learning is possible under
standard trajectory feedback. Notably, distinguishable POMDPs only require the
emission distributions from different latent states to be \emph{different}
instead of \emph{linearly independent} as required in revealing POMDPs.