  In this paper we consider the problem of remote state estimation of a
Gauss-Markov process, where a sensor can, at each discrete time instant,
transmit on one out of M different communication channels. A key difficulty of
the situation at hand is that the channel statistics are unknown. We study the
case where both learning of the channel reception probabilities and state
estimation is carried out simultaneously. Methods for choosing the channels
based on techniques for multi-armed bandits are presented, and shown to provide
stability. Furthermore, we define the performance notion of estimation regret,
and derive bounds on how it scales with time for the considered algorithms.
