Federated learning (FL) is an appealing paradigm that allows a group of machines(a.k.a. clients) to learn collectively while keeping their data local. However, dueto the heterogeneity between the clients’ data distributions, the model obtainedthrough the use of FL algorithms may perform poorly on some client’s data.Personalization addresses this issue by enabling each client to have a differentmodel tailored to their own data while simultaneously benefiting from the otherclients’ data. We consider an FL setting where some clients can be adversarial, andwe derive conditions under which full collaboration fails. Specifically, we analyzethe generalization performance of an interpolated personalized FL framework in thepresence of adversarial clients, and we precisely characterize situations when fullcollaboration performs strictly worse than fine-tuned personalization. Our analysisdetermines how much we should scale down the level of collaboration, accordingto data heterogeneity and the tolerable fraction of adversarial clients. We supportour findings with empirical results on mean estimation and binary classificationproblems, considering synthetic and benchmark image classification datasets