Distributed Linear Parameter Estimation: Asymptotically Efficient\n Adaptive Strategies

The paper considers the problem of distributed adaptive linear parameter\nestimation in multi-agent inference networks. Local sensing model information\nis only partially available at the agents and inter-agent communication is\nassumed to be unpredictable. The paper develops a generic mixed time-scale\nstochastic procedure consisting of simultaneous distributed learning and\nestimation, in which the agents adaptively assess their relative observation\nquality over time and fuse the innovations accordingly. Under rather weak\nassumptions on the statistical model and the inter-agent communication, it is\nshown that, by properly tuning the consensus potential with respect to the\ninnovation potential, the asymptotic information rate loss incurred in the\nlearning process may be made negligible. As such, it is shown that the agent\nestimates are asymptotically efficient, in that their asymptotic covariance\ncoincides with that of a centralized estimator (the inverse of the centralized\nFisher information rate for Gaussian systems) with perfect global model\ninformation and having access to all observations at all times. The proof\ntechniques are mainly based on convergence arguments for non-Markovian mixed\ntime scale stochastic approximation procedures. Several approximation results\ndeveloped in the process are of independent interest.\n