Distributed Online System Identification for LTI Systems Using Reverse Experience Replay

TL;DR

This paper introduces a distributed online system identification method for LTI systems that leverages reverse experience replay and multi-agent communication to improve estimation accuracy.

Contribution

It proposes DSGD-RER, a novel distributed algorithm extending SGD-RER for multi-agent LTI system identification, with theoretical analysis and empirical validation.

Findings

Estimation error decreases as network size increases.

DSGD-RER outperforms non-distributed methods in accuracy.

Theoretical bounds show improved error with larger networks.

Abstract

Identification of linear time-invariant (LTI) systems plays an important role in control and reinforcement learning. Both asymptotic and finite-time offline system identification are well-studied in the literature. For online system identification, the idea of stochastic-gradient descent with reverse experience replay (SGD-RER) was recently proposed, where the data sequence is stored in several buffers and the stochastic-gradient descent (SGD) update performs backward in each buffer to break the time dependency between data points. Inspired by this work, we study distributed online system identification of LTI systems over a multi-agent network. We consider agents as identical LTI systems, and the network goal is to jointly estimate the system parameters by leveraging the communication between agents. We propose DSGD-RER, a distributed variant of the SGD-RER algorithm, and theoretically characterize the improvement of the estimation error with respect to the network size. Our numerical experiments certify the reduction of estimation error as the network size grows.