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Alternating direction method of multipliers (ADMM) is a widely used tool for machine learning in distributed settings, where a machine learning model is trained over distributed data sources through an interactive process of local computation and message passing. Such an iterative process could cause privacy concerns of data owners. The goal of this paper is to provide differential privacy for ADMM-based distributed machine learning. Prior approaches on differentially private ADMM exhibit low utility under high privacy guarantee and assume the objective functions of the learning problems to be smooth and strongly convex. To address these concerns, we propose a novel differentially private ADMM-based distributed learning algorithm called DP-ADMM, which combines an approximate augmented Lagrangian function with time-varying Gaussian noise addition in the iterative process to achieve higher utility for general objective functions under the same differential privacy guarantee. We also apply the moments accountant method to analyze the end-to-end privacy loss. The theoretical analysis shows that DP-ADMM can be applied to a wider class of distributed learning problems, is provably convergent, and offers an explicit utility-privacy tradeoff. To our knowledge, this is the first paper to provide explicit convergence and utility properties for differentially private ADMM-based distributed learning algorithms. The evaluation results demonstrate that our approach can achieve good convergence and model accuracy under high end-to-end differential privacy guarantee.

A novel nano-hydroxyapatite (HA)/chitosan composite scaffold with high porosity was developed. The nano-HA particles were made in situ through a chemical method and dispersed well on the porous scaffold. They bound to the chitosan scaffolds very well. This method prevents the migration of nano-HA particles into surrounding tissues to a certain extent. The morphologies, components, and biocompatibility of the composite scaffolds were investigated. Scanning electron microscopy, porosity measurement, thermogravimetric analysis, X-ray diffraction, X-ray photoelectron spectroscopy, and Fourier transformed infrared spectroscopy were used to analyze the physical and chemical properties of the composite scaffolds. The biocompatibility was assessed by examining the proliferation and morphology of MC 3T3-E1 cells seeded on the scaffolds. The composite scaffolds showed better biocompatibility than pure chitosan scaffolds. The results suggest that the newly developed nano-HA/chitosan composite scaffolds may serve as a good three-dimensional substrate for cell attachment and migration in bone tissue engineering.