DJAM: distributed Jacobi asynchronous method for learning personal models

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. I. LEARNING PERSONAL MODELS Consider n agents, each with a personal loss function: fi : R p → R, θi 7→ fi(θi), for agent i = 1, . . . , n. For example, fi(θi) could be the loss of a model parameterized by θi on agent i’s personal dataset. The agents are the nodes of an undirected, connected network. Each agent aims to find a model that minimizes both the mismatch with its neighbors’ models and its personal loss. More specifically, agents aim to solve