  We consider federated learning (FL), where the training data is distributed
across a large number of clients. The standard optimization method in this
setting is Federated Averaging (FedAvg), which performs multiple local
first-order optimization steps between communication rounds. In this work, we
evaluate the performance of several second-order distributed methods with local
steps in the FL setting which promise to have favorable convergence properties.
  We (i) show that FedAvg performs surprisingly well against its second-order
competitors when evaluated under fair metrics (equal amount of local
computations)-in contrast to the results of previous work. Based on our
numerical study, we propose (ii) a novel variant that uses second-order local
information for updates and a global line search to counteract the resulting
local specificity.
