  We consider the federated submodel learning (FSL) problem in a distributed
storage system. In the FSL framework, the full learning model at the server
side is divided into multiple submodels such that each selected client needs to
download only the required submodel(s) and upload the corresponding update(s)
in accordance with its local training data. The server comprises multiple
independent databases and the full model is stored across these databases. An
eavesdropper passively observes all the storage and listens to all the
communicated data, of its controlled databases, to gain knowledge about the
remote client data and the submodel information. In addition, a subset of
databases may fail, negatively affecting the FSL process, as FSL process may
take a non-negligible amount of time for large models. To resolve these two
issues together (i.e., security and database repair), we propose a novel coding
mechanism coined ramp secure regenerating coding (RSRC), to store the full
model in a distributed manner. Using our new RSRC method, the eavesdropper is
permitted to learn a controllable amount of submodel information for the sake
of reducing the communication and storage costs. Further, during the database
repair process, in the construction of the replacement database, the submodels
to be updated are stored in the form of their latest version from updating
clients, while the remaining submodels are obtained from the previous version
in other databases through routing clients. Our new RSRC-based distributed FSL
approach is constructed on top of our earlier two-database FSL scheme which
uses private set union (PSU). A complete one-round FSL process consists of
FSL-PSU phase, FSL-write phase and additional auxiliary phases. Our proposed
FSL scheme is also robust against database drop-outs, client drop-outs, client
late-arrivals and an active adversary controlling databases.
