AbstractMotivated by computer networks and machine‐to‐machine communication applications, a bidirectional link is studied in which two nodes, Node 1 and Node 2, communicate to fulfill generally conflicting informational requirements. Node 2 is able to acquire information from the environment, for example, via access to a remote database or via sensing. Information acquisition is expensive in terms of system resources, for example, time, bandwidth and energy, and thus should be carried out efficiently by adapting the acquisition process to the needs of the application. As a result of the forward communication from Node 1 to Node 2, the latter wishes to compute some function, such as a suitable average, of the data available at Node 1 and of the data obtained from the environment. The forward link is also used by Node 1 to query Node 2 with the aim of retrieving suitable information from the environment on the backward link. The problem is formulated in the context of multi‐terminal rate distortion theory and the optimal trade‐off between communication rates, distortions of the information produced at the two nodes and costs for information acquisition at Node 2 is derived. The issue of robustness to possible malfunctioning of the data acquisition process at Node 2 is also investigated. The results are illustrated via an example that demonstrates the different roles played by the forward communication, namely data exchange, query and control.Copyright © 2013 John Wiley & Sons, Ltd.