Online multi-task learning (OMTL) enhances streaming data processing by leveraging the inherent relations among multiple tasks. It can be described as an optimization problem in which a single loss function is defined for multiple tasks. Existing gradient-descent-based methods for this problem might suffer from gradient vanishing and poor conditioning issues. Furthermore, the centralized setting hinders their application to online parallel optimization, which is vital to big data analytics. Therefore, this study proposes a novel OMTL framework based on the alternating direction multiplier method (ADMM), a recent breakthrough in optimization suitable for the distributed computing environment because of its decomposable and easy-to-implement nature. The relations among multiple tasks are modeled dynamically to fit the constant changes in an online scenario. In a classical distributed computing architecture with a central server, the proposed OMTL algorithm with the ADMM optimizer outperforms SGD-based approaches in terms of accuracy and efficiency. Because the central server might become a bottleneck when the data scale grows, we further tailor the algorithm to a decentralized setting, so that each node can work by only exchanging information with local neighbors. Experimental results on a synthetic and several real-world datasets demonstrate the efficiency of our methods.

Many machine learning applications require operating on a spatially distributed dataset. Despite technological advances, privacy considerations and communication constraints may prevent gathering the entire dataset in a central unit. In this paper, we propose a distributed sampling scheme based on the alternating direction method of multipliers, which is commonly used in the optimization literature due to its fast convergence. In contrast to distributed optimization, distributed sampling allows for uncertainty quantification in Bayesian inference tasks. We provide both theoretical guarantees of our algorithm's convergence and experimental evidence of its superiority to the state-of-the-art. For our theoretical results, we use convex optimization tools to establish a fundamental inequality on the generated local sample iterates. This inequality enables us to show convergence of the distribution associated with these iterates to the underlying target distribution in Wasserstein distance. In simulation, we deploy our algorithm on linear and logistic regression tasks and illustrate its fast convergence compared to existing gradient-based methods.