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This paper considers the problem of decentralized, personalized federatedlearning. For centralized personalized federated learning, a penalty thatmeasures the deviation from the local model and its average, is often added tothe objective function. However, in a decentralized setting this penalty isexpensive in terms of communication costs, so here, a different penalty - onethat is built to respect the structure of the underlying computational network- is used instead. We present lower bounds on the communication and localcomputation costs for this problem formulation and we also present provablyoptimal methods for decentralized personalized federated learning. Numericalexperiments are presented to demonstrate the practical performance of ourmethods.

Decentralized Personalized Federated Learning: Lower Bounds and Optimal Algorithm for All Personalization Modes