Learning the Linear Quadratic Regulator from Nonlinear Observations
This addresses the challenge of sample-efficient control in environments with complex observations like images, offering a foundational advance for robotics and AI applications.
The authors tackled the problem of continuous control with high-dimensional nonlinear observations by introducing the RichLQR setting and proposing the RichID algorithm, which achieves sample-efficient learning with provable guarantees scaling only with latent state dimension and decoder capacity.
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.