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.

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In this paper, a four-channel pulse-triggered functional electrical stimulator using complementary current source and time division output method is proposed for the research and application of functional electrical stimulation (FES). The high-voltage compliance and output impedance is increased by adopting the complementary current source, which can also realize the linear voltage-to-current conversion and high channel isolation. A high-voltage analog switch chip MAX14803, combined with a FIFO queue algorithm in the microprocessor, is used to setup the H-bridge and multiplexers for the four-channel time division multiplexing output. With this method, the size and cost of the key components are reduced greatly. The stimulating core circuit area is 30 × 50 mm(2). According to the experiments, the stimulator can achieve the four-channel charge-balanced biphasic stimulation with a current range between 0 and 60 mA and a single-phase pulse amplitude up to 60 V.