Simple, Private, and Accurate 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 parameters in a distributed manner while preserving the privacy of each reference. We present simple iterative methods that guarantee high accuracy (i.e. the exact asymptotic computation of the global average) and high privacy (i.e. no node can estimate another node's reference value to any meaningful degree). To achieve this, we assume that the digraph modeling the communication between nodes satisfies certain topological conditions. Other related methods in the literature also achieve high accuracy and privacy, but under topological conditions more restrictive than ours. Moreover, our method is simpler because it does not require any initial scrambling phase, it does not inject any noise or other masking signals into the distributed computation, it does not require any random switching of edge weights, and it does not rely on homomorphic encryption.