  Federated learning (FL) is an emerging machine learning paradigm involving
multiple clients, e.g., mobile phone devices, with an incentive to collaborate
in solving a machine learning problem coordinated by a central server. FL was
proposed in 2016 by Kone\v{c}n\'{y} et al. and McMahan et al. as a viable
privacy-preserving alternative to traditional centralized machine learning
since, by construction, the training data points are decentralized and never
transferred by the clients to a central server. Therefore, to a certain degree,
FL mitigates the privacy risks associated with centralized data collection.
  Unfortunately, optimization for FL faces several specific issues that
centralized optimization usually does not need to handle. In this thesis, we
identify several of these challenges and propose new methods and algorithms to
address them, with the ultimate goal of enabling practical FL solutions
supported with mathematically rigorous guarantees.
