  Federated learning (FL) is a technique that trains machine learning models
from decentralized data sources. We study FL under local notions of privacy
constraints, which provides strong protection against sensitive data
disclosures via obfuscating the data before leaving the client. We identify two
major concerns in designing practical privacy-preserving FL algorithms:
communication efficiency and high-dimensional compatibility. We then develop a
gradient-based learning algorithm called \emph{sqSGD} (selective quantized
stochastic gradient descent) that addresses both concerns. The proposed
algorithm is based on a novel privacy-preserving quantization scheme that uses
a constant number of bits per dimension per client. Then we improve the base
algorithm in three ways: first, we apply a gradient subsampling strategy that
simultaneously offers better training performance and smaller communication
costs under a fixed privacy budget. Secondly, we utilize randomized rotation as
a preprocessing step to reduce quantization error. Thirdly, an adaptive
gradient norm upper bound shrinkage strategy is adopted to improve accuracy and
stabilize training. Finally, the practicality of the proposed framework is
demonstrated on benchmark datasets. Experiment results show that sqSGD
successfully learns large models like LeNet and ResNet with local privacy
constraints. In addition, with fixed privacy and communication level, the
performance of sqSGD significantly dominates that of various baseline
algorithms.
