Node selection for probing connections in evoked dynamic networks

We consider the problem of optimal probing to learn connectivity weights in an evoked dynamic network. Such a network, in which each edge measures an input-output relationship between sites in sensor/actuator-space, is relevant to applications in neural medicine and other settings in which the underlying physical network structure is not well-known. We show that the problem of selecting which node to probe amounts to a problem of optimal sensor scheduling. In this case, the solution to the greedy probing strategy has a convenient solution. Furthermore, we show that under certain conditions, the greedy probing strategy is optimal over a finite horizon and, moreover, that it amounts to periodic `round-robin' scheduling.