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We study Reinforcement Learning for partially observable dynamical systemsusing function approximation. We propose a new \textit{Partially ObservableBilinear Actor-Critic framework}, that is general enough to include models suchas observable tabular Partially Observable Markov Decision Processes (POMDPs),observable Linear-Quadratic-Gaussian (LQG), Predictive State Representations(PSRs), as well as a newly introduced model Hilbert Space Embeddings of POMDPsand observable POMDPs with latent low-rank transition. Under this framework, wepropose an actor-critic style algorithm that is capable of performing agnosticpolicy learning. Given a policy class that consists of memory based policies(that look at a fixed-length window of recent observations), and a valuefunction class that consists of functions taking both memory and futureobservations as inputs, our algorithm learns to compete against the bestmemory-based policy in the given policy class. For certain examples such asundercomplete observable tabular POMDPs, observable LQGs and observable POMDPswith latent low-rank transition, by implicitly leveraging their specialproperties, our algorithm is even capable of competing against the globallyoptimal policy without paying an exponential dependence on the horizon in itssample complexity.

Provably Efficient Reinforcement Learning in Partially Observable Dynamical Systems