On the Sample Complexity of Decentralized Linear Quadratic Regulator with Partially Nested Information Structure

TL;DR

This paper presents a sample-efficient, model-based learning approach for decentralized linear quadratic control with partially nested information, providing theoretical guarantees on suboptimality and sample complexity.

Contribution

It introduces a method to estimate system models from limited data and designs decentralized controllers with provable performance bounds, addressing unknown system models.

Findings

Suboptimality gap scales linearly with model estimation error.

Provides an end-to-end sample complexity bound for decentralized control.

Demonstrates effectiveness of the approach in partially nested information structures.

Abstract

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.