  Decentralized learning is appealing as it enables the scalable usage of large
amounts of distributed data and resources (without resorting to any central
entity), while promoting privacy since every user minimizes the direct exposure
of their data. Yet, without additional precautions, curious users can still
leverage models obtained from their peers to violate privacy. In this paper, we
propose Decor, a variant of decentralized SGD with differential privacy (DP)
guarantees. Essentially, in Decor, users securely exchange randomness seeds in
one communication round to generate pairwise-canceling correlated Gaussian
noises, which are injected to protect local models at every communication
round. We theoretically and empirically show that, for arbitrary connected
graphs, Decor matches the central DP optimal privacy-utility trade-off. We do
so under SecLDP, our new relaxation of local DP, which protects all user
communications against an external eavesdropper and curious users, assuming
that every pair of connected users shares a secret, i.e., an information hidden
to all others. The main theoretical challenge is to control the accumulation of
non-canceling correlated noise due to network sparsity. We also propose a
companion SecLDP privacy accountant for public use.
