  We investigate contrastive learning in the federated setting through the lens
of SimCLR and multi-view mutual information maximization. In doing so, we
uncover a connection between contrastive representation learning and user
verification; by adding a user verification loss to each client's local SimCLR
loss we recover a lower bound to the global multi-view mutual information. To
accommodate for the case of when some labelled data are available at the
clients, we extend our SimCLR variant to the federated semi-supervised setting.
We see that a supervised SimCLR objective can be obtained with two changes: a)
the contrastive loss is computed between datapoints that share the same label
and b) we require an additional auxiliary head that predicts the correct labels
from either of the two views. Along with the proposed SimCLR extensions, we
also study how different sources of non-i.i.d.-ness can impact the performance
of federated unsupervised learning through global mutual information
maximization; we find that a global objective is beneficial for some sources of
non-i.i.d.-ness but can be detrimental for others. We empirically evaluate our
proposed extensions in various tasks to validate our claims and furthermore
demonstrate that our proposed modifications generalize to other pretraining
methods.
