الملخص
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.
الكلمات المفتاحية
الموضوع
بيانات النشر
- المجلة
- غير متاح
- وصول مفتوح
- وصول مفتوح أخضر
اقتبس هذه المقالة
APA 7
Labbi, S., Mangold, P., & Moulines, E. (2026). Best of Both Worlds in Federated LSA: Speedup When Possible, Personalization Always. https://omanscience.com/ar/articles/best-of-both-worlds-in-federated-lsa-speedup-when-possible-personalization-always
MLA 9
Labbi, Safwan, et al. "Best of Both Worlds in Federated LSA: Speedup When Possible, Personalization Always." https://omanscience.com/ar/articles/best-of-both-worlds-in-federated-lsa-speedup-when-possible-personalization-always.
شيكاغو (المؤلف–التاريخ)
Labbi, Safwan, Paul Mangold, and Eric Moulines. 2026. "Best of Both Worlds in Federated LSA: Speedup When Possible, Personalization Always." https://omanscience.com/ar/articles/best-of-both-worlds-in-federated-lsa-speedup-when-possible-personalization-always.
هارفارد
Labbi, S., Mangold, P. and Moulines, E. (2026) 'Best of Both Worlds in Federated LSA: Speedup When Possible, Personalization Always', Available at: https://omanscience.com/ar/articles/best-of-both-worlds-in-federated-lsa-speedup-when-possible-personalization-always.
فانكوفر
Labbi S, Mangold P, Moulines E. Best of Both Worlds in Federated LSA: Speedup When Possible, Personalization Always. https://omanscience.com/ar/articles/best-of-both-worlds-in-federated-lsa-speedup-when-possible-personalization-always
IEEE
S. Labbi, P. Mangold, and E. Moulines, "Best of Both Worlds in Federated LSA: Speedup When Possible, Personalization Always," https://omanscience.com/ar/articles/best-of-both-worlds-in-federated-lsa-speedup-when-possible-personalization-always.