# On Collaboration in Distributed Parameter Estimation with Resource Constraints

arXiv: https://arxiv.org/abs/2307.06442 · HTML: https://mlsanity.com/paper/2307.06442/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 84 references that are in the map.
- First posted on arXiv 12 Jul 2023.

## Builds on (most cited first, 10 of 10)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Inference under Information Constraints II: Communication Constraints and Shared Randomness](https://mlsanity.com/paper/1905.08302/) (2019)
- [Interactive Inference under Information Constraints](https://mlsanity.com/paper/2007.10976/) (2020)
- [Budget-Constrained Bandits over General Cost and Reward Distributions](https://mlsanity.com/paper/2003.00365/) (2020)
- [An Elementary Introduction to Kalman Filtering](https://mlsanity.com/paper/1710.04055/) (2017)
- [Order Optimal One-Shot Distributed Learning](https://mlsanity.com/paper/1911.00731/) (2019)
- [Data-driven sparse sensor placement based on A-optimal design of experiment with ADMM](https://mlsanity.com/paper/2010.09329/) (2020)
- [To Collaborate or Not in Distributed Statistical Estimation with Resource Constraints?](https://mlsanity.com/paper/2206.00111/) (2022)
- [Adaptive Designs for Optimal Observed Fisher Information](https://mlsanity.com/paper/1712.08499/) (2017)
- [Sequential Estimation under Multiple Resources: a Bandit Point of View](https://mlsanity.com/paper/2109.14703/) (2021)

## Abstract (arXiv)

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.