Alternating direction method of multiplier (ADMM) is a powerful method to solve decentralized convex optimization problems. In distributed settings, each node performs computation with its local data and the local results are exchanged among neighboring nodes in an iterative fashion. During this iterative process the leakage of data privacy arises and can accumulate significantly over many iterations, making it difficult to balance the privacy-accuracy tradeoff. We propose Recycled ADMM (R-ADMM), where a linear approximation is applied to every even iteration, its solution directly calculated using only results from the previous, odd iteration. It turns out that under such a scheme, half of the updates incur no privacy loss and require much less computation compared to the conventional ADMM. Moreover, R-ADMM can be further modified (MR-ADMM) such that each node independently determines its own penalty parameter over iterations. We obtain a sufficient condition for the convergence of both algorithms and provide the privacy analysis based on objective perturbation. It can be shown that the privacyaccuracy tradeoff can be improved significantly compared with conventional ADMM.

Alternating direction method of multiplier (ADMM) is a powerful method to solve decentralized convex optimization problems. In distributed settings, each node performs computation with its local data and the local results are exchanged among neighboring nodes in an iterative fashion. During this iterative process the leakage of data privacy arises and can accumulate significantly over many iterations, making it difficult to balance the privacy-utility tradeoff. In this study we propose Recycled ADMM (R-ADMM), where a linear approximation is applied to every even iteration, its solution directly calculated using only results from the previous, odd iteration. It turns out that under such a scheme, half of the updates incur no privacy loss and require much less computation compared to the conventional ADMM. We obtain a sufficient condition for the convergence of R-ADMM and provide the privacy analysis based on objective perturbation.

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Recognizing the factors that cause stress is a crucial step toward early detection of stressors. In this regard, several studies make an effort to recognize individuals' stress using an Electroencephalogram (EEG). However, current EEG-based stress recognition frameworks have several drawbacks. First, they are mostly designed to recognize individuals' stress only in a controlled laboratory environment. Second, they do not take into account the changes in the EEG signals of different subjects under the same stressors. Third, most of the current stress recognition algorithms occur in an offline setting. To address these issues, this study proposes an EEG-based stress recognition framework that takes into account each subject's brainwave patterns to train the stress recognition classifier and continuously update its classifier based on new input signals in near real-time. The proposed framework first removes EEG signal artifacts, then extracts a broad range of EEG signal features, and finally applies different Online Multi-Task Learning (OMTL) algorithms to recognize individuals' stress in near real time. The proposed framework was applied on the EEG collected in two environments-first on the EEG collected in a controlled lab environment using a wired-EEG and second on the EEG collected at in the field using a wearable EEG device. The OMTL-VonNeuman method resulted in the best prediction accuracy on both datasets (71.14% on the first dataset and 77.61% on second) among all tested algorithms. The proposed stress recognition framework continuously updates its classifier and therefore contributes to stress recognition for new stressful situations that are beyond the range of pre-defined stressful conditions in near real time both in a controlled lab environment and at real job sites.

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