This work introduces an alternating GD and minimization (altGDmin) based solution for solving the meta learning problem (few-shot learning by multi-task representation learning). Our main contribution is the development of a provably secure (Byzantine-resilient) altGDmin algorithm for solving this problem in a federated setting. We argue that our solution is sample efficient, fast, and communication-efficient. In solving this problem, we also introduce a novel secure solution to the federated subspace learning meta-problem that occurs in many different applications.