Removing sampling bias in networked stochastic approximation

We consider a stochastic approximation algorithm implemented on a network of computing elements corresponding to the nodes of a connected graph wherein each node polls one or more of its neighbors at random and pulls the relevant data from there. A blind implementation suffers from `sampling bias´ whereby each node´s contribution to the computation gets weighed by its frequency of being polled. We propose a modified step size schedule that works around this problem. As an example, we propose a modification of an existing scheme for reputation systems that removes such a bias therein.