Private and Hot-Pluggable Distributed Averaging

Some distributed optimization applications require privacy, meaning that the values of certain parameters local to a node should not be revealed to other nodes in the network during the joint optimization process. A special case is the problem of private distributed averaging, in which a network of nodes computes the global average of individual node reference values in a distributed manner while preserving the privacy of each reference. We present simple iterative methods that guarantee accuracy (i.e., the exact asymptotic computation of the global average) and privacy (i.e., no node can estimate another node's reference value). To achieve this, we require that the digraph modeling the communication between nodes satisfy certain topological conditions. Our method is hot-pluggable (meaning no reinitialization of the averaging process is required when the network changes or a node enters or leaves, when there is a communication or computation fault, or when a node's reference value changes); it does not require an initial scrambling phase; it does not inject noise or other masking signals into the distributed computation; it does not require random switching of edge weights; and it does not rely on homomorphic encryption.