Ivan Agarský

Laurent Condat, Ivan Agarský, Peter Richtárik

In federated learning, a large number of users are involved in a global learning task, in a collaborative way. They alternate local computations and two-way communication with a distant orchestrating server. Communication, which can be slow and costly, is the main bottleneck in this setting. To reduce the communication load and therefore accelerate distributed gradient descent, two strategies are popular: 1) communicate less frequently; that is, perform several iterations of local computations between the communication rounds; and 2) communicate compressed information instead of full-dimensional vectors. We propose the first algorithm for distributed optimization and federated learning, which harnesses these two strategies jointly and converges linearly to an exact solution in the strongly convex setting, with a doubly accelerated rate: our algorithm benefits from the two acceleration mechanisms provided by local training and compression, namely a better dependency on the condition number of the functions and on the dimension of the model, respectively.

Laurent Condat, Ivan Agarský, Grigory Malinovsky et al.

In distributed optimization and learning, several machines alternate between local computations in parallel and communication with a distant server. Communication is usually slow and costly and forms the main bottleneck. This is particularly true in federated learning, where a large number of users collaborate toward a global training task. In addition, it is desirable for a robust algorithm to allow for partial participation, since it is often the case that some clients are not able to participate to the entire process and are idle at certain times. Two strategies are popular to reduce the communication burden: 1) local training, which consists in communicating less frequently, or equivalently performing more local computations between the communication rounds; and 2) compression, whereby compressed information instead of full-dimensional vectors is communicated. We propose TAMUNA, the first algorithm for distributed optimization that leveraged the two strategies of local training and compression jointly and allows for partial participation. In the strongly convex setting, TAMUNA converges linearly to the exact solution and provably benefits from the two mechanisms: it exhibits a doubly-accelerated convergence rate, with respect to the condition number of the functions and the model dimension.