Machine learning requires large amounts of data, which is increasingly distributed over many systems (user devices, independent storage systems). Unfortunately aggregating this data in one site for learning is not always practical, either because of network costs or privacy concerns. Decentralized machine learning holds the potential to address these concerns, but unfortunately, most approaches proposed so far for distributed learning with neural network are mono-task, and do not transfer easily to multi-tasks problems, for which users seek to solve related but distinct learning tasks and the few existing multi-task approaches have serious limitations. In this paper, we propose a novel learning method for neural networks that is decentralized, multi-task, and keeps users' data local. Our approach works with different learning algorithms, on various types of neural networks. We formally analyze the convergence of our method, and we evaluate its efficiency in different situations on various kind of neural networks, with different learning algorithms, thus demonstrating its benefits in terms of learning quality and convergence.