Learning the Linear Quadratic Regulator from Nonlinear Observations

TL;DR

This paper presents RichLQR, a new control setting with high-dimensional nonlinear observations, and introduces RichID, an algorithm that efficiently learns near-optimal policies with provable guarantees.

Contribution

The paper proposes RichLQR, a novel problem setting, and introduces RichID, a sample-efficient, oracle-efficient algorithm with theoretical guarantees for nonlinear observation-based control.

Findings

RichID achieves near-optimal control with sample complexity depending only on latent state dimension.

First provable guarantees for continuous control with unknown nonlinearities and function approximation.

Algorithm is oracle-efficient, relying on least-squares regression for decoder class access.

Abstract

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.