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Convergence bounds are one of the main tools to obtain information on theperformance of a distributed machine learning task, before running the taskitself. In this work, we perform a set of experiments to assess to whichextent, and in which way, such bounds can predict and improve the performanceof real-world distributed (namely, federated) learning tasks. We find that, ascan be expected given the way they are obtained, bounds are quite loose andtheir relative magnitude reflects the training rather than the testing loss.More unexpectedly, we find that some of the quantities appearing in the boundsturn out to be very useful to identify the clients that are most likely tocontribute to the learning process, without requiring the disclosure of anyinformation about the quality or size of their datasets. This suggests thatfurther research is warranted on the ways -- often counter-intuitive -- inwhich convergence bounds can be exploited to improve the performance ofreal-world distributed learning tasks.

Unexpectedly Useful: Convergence Bounds And Real-World Distributed Learning