  We consider a set of learning agents in a collaborative peer-to-peer network,
where each agent learns a personalized model according to its own learning
objective. The question addressed in this paper is: how can agents improve upon
their locally trained model by communicating with other agents that have
similar objectives? We introduce and analyze two asynchronous gossip algorithms
running in a fully decentralized manner. Our first approach, inspired from
label propagation, aims to smooth pre-trained local models over the network
while accounting for the confidence that each agent has in its initial model.
In our second approach, agents jointly learn and propagate their model by
making iterative updates based on both their local dataset and the behavior of
their neighbors. To optimize this challenging objective, our decentralized
algorithm is based on ADMM.
