Abstract: Methods, systems, and apparatus, including computer programs encoded on computer storage media, for training a machine learning model having a set of local model parameters and a set of global model parameters under a partially local federated learning framework. One of the methods include maintaining local data and data defining the local model parameters; receiving data defining current values of the global model parameters; determining, based on the local data, the local model parameters, and the current values of the global model parameters, current values of the local model parameters; determining, based on the local data, the current values of the local model parameters, and the current values of the global model parameters, updated values of the global model parameters; generating, based on the updated values of the global model parameters, parameter update data defining an update to the global model parameters; and transmitting the parameter update data.