On the Sample Complexity of Decentralized Linear Quadratic Regulator with Partially Nested Information Structure
This work addresses the challenge of learning decentralized controllers for control systems with partial information, which is incremental as it extends known methods to a specific information structure.
The paper tackles the problem of designing decentralized control policies for linear quadratic regulators with partially nested information when the system model is unknown, proposing a model-based learning approach that estimates the model from data and designs a policy, with results showing the suboptimality gap scales linearly with estimation error and providing an end-to-end sample complexity analysis.
We study the problem of control policy design for decentralized state-feedback linear quadratic control with a partially nested information structure, when the system model is unknown. We propose a model-based learning solution, which consists of two steps. First, we estimate the unknown system model from a single system trajectory of finite length, using least squares estimation. Next, based on the estimated system model, we design a control policy that satisfies the desired information structure. We show that the suboptimality gap between our control policy and the optimal decentralized control policy (designed using accurate knowledge of the system model) scales linearly with the estimation error of the system model. Using this result, we provide an end-to-end sample complexity result for learning decentralized controllers for a linear quadratic control problem with a partially nested information structure.