arXiv：cs.LG· Safwan Labbi, Paul Mangold, Eric Moulines·· 3 小时前
PF-LSA：联邦 LSA 兼顾线性加速与个性化
Best of Both Worlds in Federated LSA: Speedup When Possible, Personalization Always
AI 导读
研究者提出 PF-LSA，一种将各智能体本地随机更新与全局平均更新混合的极简算法，用于个性化联邦线性随机逼近（LSA）与个性化时序差分学习。无需预先知道异构程度，PF-LSA 即可收敛到每个智能体的个性化解，并在学习问题足够相似时实现随智能体数量的线性加速，且相比标准联邦方法不增加额外计算开销。
正文
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.
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2610.11555 [cs.LG] |
| (or arXiv:2610.11555v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2610.11555 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Safwan Labbi [view email]
[v1]
Thu, 8 Oct 2026 09:18:53 UTC (153 KB)
来源：arXiv：cs.LG · arxiv.org