Private Non-Convex Federated Learning Without a Trusted Server
release_5ouauuw7bbf6doobre7ynuj544
by
Andrew Lowy, Ali Ghafelebashi, Meisam Razaviyayn
2022
Abstract
We study differentially private (DP) federated learning (FL) with non-convex
loss functions and heterogeneous (non-i.i.d.) client data in the absence of a
trusted server, both with and without a secure "shuffler" to anonymize client
reports. We propose novel algorithms that satisfy local differential privacy
(LDP) at the client level and shuffle differential privacy (SDP) for three
classes of Lipschitz continuous loss functions: First, we consider losses
satisfying the Proximal Polyak-Lojasiewicz (PL) inequality, which is an
extension of the classical PL condition to the constrained setting. Prior works
studying DP PL optimization only consider the unconstrained problem with
Lipschitz loss functions, which rules out many interesting practical losses,
such as strongly convex, least squares, and regularized logistic regression.
However, by analyzing the proximal PL scenario, we permit such losses which are
Lipschitz on a restricted parameter domain. We propose LDP and SDP algorithms
that nearly attain the optimal strongly convex, homogeneous (i.i.d.) rates.
Second, we provide the first DP algorithms for non-convex/non-smooth loss
functions. Third, we specialize our analysis to smooth, unconstrained
non-convex FL. Our bounds improve on the state-of-the-art, even in the special
case of a single client, and match the non-private lower bound in certain
practical parameter regimes. Numerical experiments show that our algorithm
yields better accuracy than baselines for most privacy levels.
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