X-Secure T-Private Federated Submodel Learning

The problem of (information-theoretic) X-secure T-private federated submodel learning represents a setting where a large scale machine learning model is partitioned into K submodels and stored across N distributed servers according to an X-secure threshold secret sharing scheme. Various users wish to successively train (update) the submodel that is most relevant to their local data while keeping the identity of their relevant submodel private from any set of up to T colluding servers. Inspired by the idea of cross-subspace alignment (CSA) for X - secure T -private information retrieval, we propose a novel CSA-RW (read-write) scheme for efficiently (in communication cost) and privately reading from and writing to a distributed database. CSA-RW improves significantly upon available baselines from prior work and is shown to be asymptotically/approximately optimal in download/upload cost. It also answers an open question previously noted by Kairouz et al. by exploiting synergistic gains from the joint design of private read-write.