Classical consensus-based strategies for federated and decentralized learning are statistically suboptimal in the presence of heterogeneous local data or task distributions. As a result, in recent years, there has been growing interest in multitask or personalized strategies, which allow individual agents to benefit from one another in pursuing locally optimal models without enforcing consensus. Existing strategies require either precise prior knowledge of the underlying task relationships or are fully non-parametric and instead rely on meta-learning or proximal constructions. In this work, we introduce an algorithmic framework that strikes a balance between these extremes. By modeling task relationships through a Gaussian Markov Random Field with an unknown precision matrix, we develop a strategy that jointly learns both the task relationships and the local models, allowing agents to self-organize in a way consistent with their individual data distributions. Our theoretical analysis quantifies the quality of the learned relationship, and our numerical experiments demonstrate its practical effectiveness.

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