Distributed signal cancelation inspired by Witsenhausen´s counterexample

We consider the problem of two-stage signal cancelation based on noisy observations. This problem turns out to be an extension of the Witsenhausen counterexample - a famous open problem in distributed control. Cost is imposed on the power expended by the first controller, and the residual signal after the actions of the two controllers. Along the lines of a recent approximate solution to the Witsenhausen counterexample, we provide an approximate solution to this distributed signal cancelation problem to within a constant factor. This approximation holds uniformly over all problem parameters and for all vector lengths.