  We introduce a new problem setting for continuous control called the LQR with
Rich Observations, or RichLQR. In our setting, the environment is summarized by
a low-dimensional continuous latent state with linear dynamics and quadratic
costs, but the agent operates on high-dimensional, nonlinear observations such
as images from a camera. To enable sample-efficient learning, we assume that
the learner has access to a class of decoder functions (e.g., neural networks)
that is flexible enough to capture the mapping from observations to latent
states. We introduce a new algorithm, RichID, which learns a near-optimal
policy for the RichLQR with sample complexity scaling only with the dimension
of the latent state space and the capacity of the decoder function class.
RichID is oracle-efficient and accesses the decoder class only through calls to
a least-squares regression oracle. Our results constitute the first provable
sample complexity guarantee for continuous control with an unknown nonlinearity
in the system model and general function approximation.
