Distributed Discrete-time Optimization in Multi-agent Networks Using only Sign of Relative State

TL;DR

This paper introduces distributed discrete-time algorithms for multi-agent network optimization that rely solely on the sign of relative state information, maintaining convergence speed despite limited data.

Contribution

The paper presents novel algorithms using only sign information of relative states, with theoretical convergence analysis and robustness to noise and random graph activation.

Findings

Convergence speed comparable to algorithms using full relative state info

Robustness to noise in relative state measurements

Validated on distributed quantile regression problems

Abstract

This paper proposes distributed discrete-time algorithms to cooperatively solve an additive cost optimization problem in multi-agent networks. The striking feature lies in the use of only the sign of relative state information between neighbors, which substantially differentiates our algorithms from others in the existing literature. We first interpret the proposed algorithms in terms of the penalty method in optimization theory and then perform non-asymptotic analysis to study convergence for static network graphs. Compared with the celebrated distributed subgradient algorithms, which however use the exact relative state information, the convergence speed is essentially not affected by the loss of information. We also study how introducing noise into the relative state information and randomly activated graphs affect the performance of our algorithms. Finally, we validate the theoretical results on a class of distributed quantile regression problems.