Best of Both Worlds in Federated LSA: Speedup When Possible, Personalization Always

Abstract:We study personalized federated linear stochastic approximation (LSA), a framework which notably encompass personalized temporal difference learning. In this setting, heterogeneous agents collaborate to solve distinct linear fixed-point equations, each corresponding to an agent-specific learning problem. A central open question in personalized learning is whether a single method can adapt to an unknown level of heterogeneity by converging to each agent's personalized solution in all regimes while achieving a linear speedup in the number of agents when their learning problems are sufficiently similar. We answer this question affirmatively by introducing PF-LSA, a minimalist algorithm that mixes each agent's local stochastic update with the average update across agents, at no additional computational cost relative to standard federated methods. We prove that PF-LSA, achieves best-of-both-worlds guarantees without any prior knowledge on the level of heterogeneity. Our analysis is based on a sharp decomposition of the error into consensus and disagreement components. The consensus error decays rapidly, whereas the disagreement error decays more slowly but becomes negligible in low-heterogeneity regimes.

Machine Learning (cs.LG)

arXiv:2610.11555 [cs.LG]

(or arXiv:2610.11555v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2610.11555 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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