Distributed Estimation of Dynamic Parameters : Regret Analysis
  This paper addresses the estimation of a time- varying parameter in a network. A group of agents sequentially receive noisy signals about the parameter (or moving target), which does not follow any particular dynamics. The parameter is not observable to an individual agent, but it is globally identifiable for the whole network. Viewing the problem with an online optimization lens, we aim to provide the finite-time or non-asymptotic analysis of the problem. To this end, we use a notion of dynamic regret which suits the online, non-stationary nature of the problem. In our setting, dynamic regret can be recognized as a finite-time counterpart of stability in the mean- square sense. We develop a distributed, online algorithm for tracking the moving target. Defining the path-length as the consecutive differences between target locations, we express an upper bound on regret in terms of the path-length of the target and network errors. We further show the consistency of the result with static setting and noiseless observations. 
Shahin Shahrampour, Alexander Rakhlin, Ali Jadbabaie
math.OC cs.LG cs.SI