Remote Estimation of Markov Processes over Costly Channels: On the Benefits of Implicit Information

In this paper, we study the remote estimation problem of a Markov process over a channel with a cost. We formulate this problem as an infinite horizon optimization problem with two players, i.e., a sensor and a monitor, that have distinct information, and with a reward function that takes into account both the communication cost and the estimation quality. We show that the main challenge in solving this problem is associated with the consideration of implicit information, i.e., information that the monitor can obtain about the source when the sensor is silent. Our main objective is to develop a framework for finding solutions to this problem without neglecting implicit information a priori. To that end, we propose three different algorithms. The first one is an alternating policy algorithm that converges to a Nash equilibrium. The second one is an occupancy-state algorithm that is guaranteed to find a globally optimal solution. The last one is a heuristic algorithm that is able to find a near-optimal solution.