Distributed Adaptive Spatial Filtering with Inexact Local Solvers

TL;DR

This paper extends the Distributed Adaptive Signal Fusion framework to work with inexact local solvers, providing convergence guarantees and validating the approach through numerical simulations in resource-constrained distributed sensing systems.

Contribution

It offers convergence and optimality analysis for DASF with inexact solvers like gradient descent, which was previously only studied with exact solvers.

Findings

Convergence is guaranteed under specific conditions for inexact local solvers.

A lower bound on the convergence rate is established.

Numerical simulations confirm the theoretical results.

Abstract

The Distributed Adaptive Signal Fusion (DASF) framework is a meta-algorithm for computing data-driven spatial filters in a distributed sensing platform with limited bandwidth and computational resources, such as a wireless sensor network. The convergence and optimality of the DASF algorithm has been extensively studied under the assumption that an exact, but possibly impractical solver for the local optimization problem at each updating node is available. In this work, we provide convergence and optimality results for the DASF framework when used with an inexact, finite-time solver such as (proximal) gradient descent or Newton's method. We provide sufficient conditions that the solver should satisfy in order to guarantee convergence of the resulting algorithm, and a lower bound for the convergence rate. We also provide numerical simulations to validate these theoretical results.