Double-Opportunity Estimation via Altruism

TL;DR

This paper introduces a new cooperative estimation method based on altruism, allowing two agents to estimate parameters with improved performance even if only one agent performs well, especially in ill-conditioned problems.

Contribution

It proposes a novel altruistic framework for cooperative estimation, generalizing MMSE, with explicit solutions in the Gaussian case and analysis of performance benefits.

Findings

Performance improvement depends on covariance matrix spectrum

Method is especially effective in ill-conditioned problems

Solution in Gaussian case involves eigenvalue computation

Abstract

A novel approach, based on the notion of altruism, is presented to cooperative parameter estimation in a system comprising two information-sharing agents. The underlying assumption is that the overall two-agent scheme can reach desired performance level even if only one of the agents performs satisfactorily, hence there exist two independent opportunities to estimate. The notion of altruism motivates a new definition of cooperative estimation optimality that generalizes the common definition of minimum mean squared error optimality. Fundamental equations are derived for two types of altruistic cooperative estimation problems, corresponding to heterarchical and hierarchical setups. Although these equations are, generally, hard to solve, their solution in the Gaussian case is straightforward and only entails the computation of the largest eigenvalue of the conditional covariance matrix and its corresponding eigenvector. Moreover, in the Gaussian case the performance improvement of the two altruistic cooperative estimation techniques over the conventional (egoistic) estimation approach is shown to depend on the problem's dimensionality and statistical distribution. In particular, the performance improvement grows with the dispersion of the spectrum of the conditional covariance matrix, rendering the new estimation approach especially appealing in ill-conditioned problems. The validity of the solution in the Gaussian case is illustrated numerically.