Collaborative Estimation of Real Valued Function by Two Agents and a Fusion Center with Knowledge Exchange

TL;DR

This paper introduces a collaborative iterative algorithm for two agents and a fusion center to estimate a real-valued function within RKHS spaces, proving its consistency and convergence under certain conditions.

Contribution

It develops a novel collaborative estimation algorithm with proven consistency for real-valued functions in RKHS, incorporating knowledge exchange between agents and a fusion center.

Findings

The algorithm is consistent with convergent subsequences.

Estimation operators are constructed and analyzed for boundedness.

Sufficient conditions for convergence are established.

Abstract

We consider a collaborative iterative algorithm with two agents and a fusion center for estimation of a real valued function (or ``model") on the set of real numbers. While the data collected by the agents is private, in every iteration of the algorithm, the models estimated by the agents are uploaded to the fusion center, fused, and, subsequently downloaded by the agents. We consider the estimation spaces at the agents and the fusion center to be Reproducing Kernel Hilbert Spaces (RKHS). Under suitable assumptions on these spaces, we prove that the algorithm is consistent, i.e., there exists a subsequence of the estimated models which converges to a model in the strong topology. To this end, we define estimation operators for the agents, fusion center, and, for every iteration of the algorithm constructively. We define valid input data sequences, study the asymptotic properties of the norm of the estimation operators, and, find sufficient conditions under which the estimation operator until any iteration is uniformly bounded. Using these results, we prove the existence of an estimation operator for the algorithm which implies the consistency of the considered estimation algorithm.