  Federated learning is a machine learning protocol that enables a large
population of agents to collaborate over multiple rounds to produce a single
consensus model. There are several federated learning applications where agents
may choose to defect permanently$-$essentially withdrawing from the
collaboration$-$if they are content with their instantaneous model in that
round. This work demonstrates the detrimental impact of such defections on the
final model's robustness and ability to generalize. We also show that current
federated optimization algorithms fail to disincentivize these harmful
defections. We introduce a novel optimization algorithm with theoretical
guarantees to prevent defections while ensuring asymptotic convergence to an
effective solution for all participating agents. We also provide numerical
experiments to corroborate our findings and demonstrate the effectiveness of
our algorithm.
