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We study federated learning (FL) -- especially cross-silo FL -- withnon-convex loss functions and data from people who do not trust the server orother silos. In this setting, each silo (e.g. hospital) must protect theprivacy of each person's data (e.g. patient's medical record), even if theserver or other silos act as adversarial eavesdroppers. To that end, weconsider inter-silo record-level (ISRL) differential privacy (DP), whichrequires silo~$i$'s communications to satisfy record/item-level DP. We proposenovel ISRL-DP algorithms for FL with heterogeneous (non-i.i.d.) silo data andtwo classes of Lipschitz continuous loss functions: First, we consider lossessatisfying the Proximal Polyak-Lojasiewicz (PL) inequality, which is anextension of the classical PL condition to the constrained setting. In contrastto our result, prior works only considered unconstrained private optimizationwith Lipschitz PL loss, which rules out most interesting PL losses such asstrongly convex problems and linear/logistic regression. Our algorithms nearlyattain the optimal strongly convex, homogeneous (i.i.d.) rate for ISRL-DP FLwithout assuming convexity or i.i.d. data. Second, we give the first privatealgorithms for non-convex non-smooth loss functions. Our utility bounds evenimprove on the state-of-the-art bounds for smooth losses. We complement ourupper bounds with lower bounds. Additionally, we provide shuffle DP (SDP)algorithms that improve over the state-of-the-art central DP algorithms undermore practical trust assumptions. Numerical experiments show that our algorithmhas better accuracy than baselines for most privacy levels. All the codes arepublicly available at:https://github.com/ghafeleb/Private-NonConvex-Federated-Learning-Without-a-Trusted-Server.

Private Non-Convex Federated Learning Without a Trusted Server