Optimal Task Assignment for Heterogeneous Federated Learning Devices

Federated Learning provides new opportunities for training machine learning models while respecting data privacy. This technique is based on heterogeneous devices that work together to iteratively train a model while never sharing their own data. Given the synchronous nature of this training, the performance of Federated Learning systems is dictated by the slowest devices, also known as stragglers. In this paper, we investigate the problem of minimizing the duration of Federated Learning rounds by controlling how much data each device uses for training. We formulate this as a makespan minimization problem with identical, independent, and atomic tasks that have to be assigned to heterogeneous resources with non-decreasing cost functions, while also respecting lower and upper limits of tasks per resource. Based on this formulation, we propose a polynomial-time algorithm named OLAR and prove that it provides optimal schedules. We evaluate OLAR in an extensive series of experiments using simulation that includes comparisons to other algorithms from the state of the art, and new extensions to them. Our results indicate that OLAR provides optimal solutions with a small execution time. They also show that the presence of lower and upper limits of tasks per resource erase any benefits that suboptimal heuristics could provide in terms of algorithm execution time.