  Federated learning (FL) is a collaborative learning paradigm that allows
different clients to train one powerful global model without sharing their
private data. Although FL has demonstrated promising results in various
applications, it is known to suffer from convergence issues caused by the data
distribution shift across different clients, especially on non-independent and
identically distributed (non-IID) data. In this paper, we study the convergence
of FL on non-IID data and propose a novel \emph{Dog Walking Theory} to
formulate and identify the missing element in existing research. The Dog
Walking Theory describes the process of a dog walker leash walking multiple
dogs from one side of the park to the other. The goal of the dog walker is to
arrive at the right destination while giving the dogs enough exercise (i.e.,
space exploration). In FL, the server is analogous to the dog walker while the
clients are analogous to the dogs. This analogy allows us to identify one
crucial yet missing element in existing FL algorithms: the leash that guides
the exploration of the clients. To address this gap, we propose a novel FL
algorithm \emph{FedWalk} that leverages an external easy-to-converge task at
the server side as a \emph{leash task} to guide the local training of the
clients. We theoretically analyze the convergence of FedWalk with respect to
data heterogeneity (between server and clients) and task discrepancy (between
the leash and the original tasks). Experiments on multiple benchmark datasets
demonstrate the superiority of FedWalk over state-of-the-art FL methods under
both IID and non-IID settings.
