  Federated learning is a useful framework for centralized learning from
distributed data under practical considerations of heterogeneity, asynchrony,
and privacy. Federated architectures are frequently deployed in deep learning
settings, which generally give rise to non-convex optimization problems.
Nevertheless, most existing analysis are either limited to convex loss
functions, or only establish first-order stationarity, despite the fact that
saddle-points, which are first-order stationary, are known to pose bottlenecks
in deep learning. We draw on recent results on the second-order optimality of
stochastic gradient algorithms in centralized and decentralized settings, and
establish second-order guarantees for a class of federated learning algorithms.

Machine Learning;Multiagent Systems;Signal Processing;Optimization and Control;Machine Learning