Double-Opportunity Estimation via Altruism
For multi-agent estimation systems, this work provides a new cooperative optimality criterion and demonstrates potential gains in ill-conditioned problems, though the results are limited to Gaussian cases and specific setups.
The paper introduces an altruistic cooperative estimation framework where only one of two agents needs to perform well, deriving optimality conditions and showing that in Gaussian settings the performance improvement over conventional estimation depends on the spectral dispersion of the conditional covariance matrix, with gains in ill-conditioned problems.
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.