We consider a distributed empirical risk minimization (ERM) optimization problem with communication efficiency and privacy requirements, motivated by the federated learn- ing (FL) framework. We propose a distributed communication-efficient and local differentially private stochastic gradient descent (CLDP-SGD) algorithm and analyze its communication, privacy, and convergence trade-offs. Since each iteration of the CLDP- SGD aggregates the client-side local gradients, we develop (optimal) communication-efficient schemes for mean estimation for several lp spaces under local differential privacy (LDP). To overcome performance limitation of LDP, CLDP-SGD takes advantage of the inherent privacy amplification provided by client sub- sampling and data subsampling at each se- lected client (through SGD) as well as the recently developed shuffled model of privacy. For convex loss functions, we prove that the proposed CLDP-SGD algorithm matches the known lower bounds on the centralized private ERM while using a finite number of bits per iteration for each client, i.e., effectively get- ting communication efficiency for “free”. We also provide preliminary experimental results supporting the theory.
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Graphical Convergence of Subgradients in Nonconvex Optimization and Learning
We investigate the stochastic optimization problem of minimizing population risk, where the loss defining the risk is assumed to be weakly convex. Compositions of Lipschitz convex functions with smooth maps are the primary examples of such losses. We analyze the estimation quality of such nonsmooth and nonconvex problems by their sample average approximations. Our main results establish dimension-dependent rates on subgradient estimation in full generality and dimension-independent rates when the loss is a generalized linear model. As an application of the developed techniques, we analyze the nonsmooth landscape of a robust nonlinear regression problem.
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- NSF-PAR ID:
- 10338310
- Date Published:
- Journal Name:
- Mathematics of Operations Research
- Volume:
- 47
- Issue:
- 1
- ISSN:
- 0364-765X
- Page Range / eLocation ID:
- 209 to 231
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1287/moor.2021.1126
