  We examine an important setting for engineered systems in which low-power
distributed sensors are each making highly noisy measurements of some unknown
target function. A center wants to accurately learn this function by querying a
small number of sensors, which ordinarily would be impossible due to the high
noise rate. The question we address is whether local communication among
sensors, together with natural best-response dynamics in an
appropriately-defined game, can denoise the system without destroying the true
signal and allow the center to succeed from only a small number of active
queries. By using techniques from game theory and empirical processes, we prove
positive (and negative) results on the denoising power of several natural
dynamics. We then show experimentally that when combined with recent agnostic
active learning algorithms, this process can achieve low error from very few
queries, performing substantially better than active or passive learning
without these denoising dynamics as well as passive learning with denoising.
