  Federated learning provides a framework to address the challenges of
distributed computing, data ownership and privacy over a large number of
distributed clients with low computational and communication capabilities. In
this paper, we study the problem of learning the exact support of sparse linear
regression in the federated learning setup. We provide a simple communication
efficient algorithm which only needs one-shot communication with the
centralized server to compute the exact support. Our method does not require
the clients to solve any optimization problem and thus, can be run on devices
with low computational capabilities. Our method is naturally robust to the
problems of client failure, model poisoning and straggling clients. We formally
prove that our method requires a number of samples per client that is
polynomial with respect to the support size, but independent of the dimension
of the problem. We require the number of distributed clients to be logarithmic
in the dimension of the problem. If the predictor variables are mutually
independent then the overall sample complexity matches the optimal sample
complexity of the non-federated centralized setting. Furthermore, our method is
easy to implement and has an overall polynomial time complexity.
