On Collaboration in Distributed Parameter Estimation with Resource Constraints

TL;DR

This paper investigates optimal resource allocation strategies for distributed sensors estimating multivariate Gaussian parameters, balancing local sampling and collaboration, with analytical solutions and learning algorithms for unknown correlations.

Contribution

It introduces a Fisher information-based framework for resource-efficient collaboration in distributed estimation, including analytical results and bandit-based learning methods for unknown correlations.

Findings

Optimal policies depend on correlation knowledge.

Analytical solutions for known correlations.

Bandit algorithms effectively learn policies when correlations are unknown.

Abstract

Effective resource allocation in sensor networks, IoT systems, and distributed computing is essential for applications such as environmental monitoring, surveillance, and smart infrastructure. Sensors or agents must optimize their resource allocation to maximize the accuracy of parameter estimation. In this work, we consider a group of sensors or agents, each sampling from a different variable of a multivariate Gaussian distribution and having a different estimation objective. We formulate a sensor or agent's data collection and collaboration policy design problem as a Fisher information maximization (or Cramer-Rao bound minimization) problem. This formulation captures a novel trade-off in energy use, between locally collecting univariate samples and collaborating to produce multivariate samples. When knowledge of the correlation between variables is available, we analytically identify two cases: (1) where the optimal data collection policy entails investing resources to transfer information for collaborative sampling, and (2) where knowledge of the correlation between samples cannot enhance estimation efficiency. When knowledge of certain correlations is unavailable, but collaboration remains potentially beneficial, we propose novel approaches that apply multi-armed bandit algorithms to learn the optimal data collection and collaboration policy in our sequential distributed parameter estimation problem. We illustrate the effectiveness of the proposed algorithms, DOUBLE-F, DOUBLE-Z, UCB-F, UCB-Z, through simulation.