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We investigate the problem of private read update write (PRUW) in relation toprivate federated submodel learning (FSL), where a machine learning model isdivided into multiple submodels based on the different types of data used totrain the model. In PRUW, each user downloads the required submodel withoutrevealing its index in the reading phase, and uploads the updates of thesubmodel without revealing the submodel index or the values of the updates inthe writing phase. In this work, we first provide a basic communicationefficient PRUW scheme, and study further means of reducing the communicationcost via sparsification. Gradient sparsification is a widely used concept inlearning applications, where only a selected set of parameters is downloadedand updated, which significantly reduces the communication cost. In this paper,we study how the concept of sparsification can be incorporated in private FSLwith the goal of reducing the communication cost, while guaranteeinginformation theoretic privacy of the updated submodel index as well as thevalues of the updates. To this end, we introduce two schemes: PRUW with top $r$sparsification and PRUW with random sparsification. The former communicatesonly the most significant parameters/updates among the servers and the users,while the latter communicates a randomly selected set of parameters/updates.The two proposed schemes introduce novel techniques such as parameter/update(noisy) permutations to handle the additional sources of information leakage inPRUW caused by sparsification. Both schemes result in significantly reducedcommunication costs compared to that of the basic (non-sparse) PRUW scheme.

Private Read Update Write (PRUW) in Federated Submodel Learning (FSL): Communication Efficient Schemes With and Without Sparsification