  We study sensor/agent data collection and collaboration policies for
parameter estimation, accounting for resource constraints and correlation
between observations collected by distinct sensors/agents. Specifically, we
consider a group of sensors/agents each samples from different variables of a
multivariate Gaussian distribution and has different estimation objectives, and
we formulate a sensor/agent's data collection and collaboration policy design
problem as a Fisher information maximization (or Cramer-Rao bound minimization)
problem. When the knowledge of correlation between variables is available, we
analytically identify two particular scenarios: (1) where the knowledge of the
correlation between samples cannot be leveraged for collaborative estimation
purposes and (2) where the optimal data collection policy involves investing
scarce resources to collaboratively sample and transfer information that is not
of immediate interest and whose statistics are already known, with the sole
goal of increasing the confidence on the estimate of the parameter of interest.
When the knowledge of certain correlation is unavailable but collaboration may
still be worthwhile, we propose novel ways to apply multi-armed bandit
algorithms to learn the optimal data collection and collaboration policy in our
distributed parameter estimation problem and demonstrate that the proposed
algorithms, DOUBLE-F, DOUBLE-Z, UCB-F, UCB-Z, are effective through
simulations.
