  Processing data collected by a network of agents often boils down to solving
an optimization problem. The distributed nature of these problems calls for
methods that are, themselves, distributed. While most collaborative learning
problems require agents to reach a common (or consensus) model, there are
situations in which the consensus solution may not be optimal. For instance,
agents may want to reach a compromise between agreeing with their neighbors and
minimizing a personal loss function. We present DJAM, a Jacobi-like distributed
algorithm for learning personalized models. This method is
implementation-friendly: it has no hyperparameters that need tuning, it is
asynchronous, and its updates only require single-neighbor interactions. We
prove that DJAM converges with probability one to the solution, provided that
the personal loss functions are strongly convex and have Lipschitz gradient. We
then give evidence that DJAM is on par with state-of-the-art methods: our
method reaches a solution with error similar to the error of a carefully tuned
ADMM in about the same number of single-neighbor interactions.
