发表机构
CNRS; École Polytechnique; Institut Polytechnique de Paris; Mohamed bin Zayed University of Artificial Intelligence; EPITA（法国国家科学研究中心; 巴黎综合理工学院; 巴黎理工学院; 穆罕默德·本·扎耶德人工智能大学; 高等计算机与技术学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对个性化联邦线性随机近似问题，提出PF-LSA算法，结合智能体局部更新与平均更新，无需异构程度先验知识，可在相似问题时提速，实现两全其美的收敛保证。
AI 中文摘要
我们研究个性化联邦线性随机近似（LSA），该框架尤其涵盖个性化时间差分学习。在此设定下，异构智能体协作求解不同的线性不动点方程，每个方程对应一个智能体特有的学习问题。个性化学习中的一个核心开放问题是：是否存在单一方法，能在所有场景下收敛至各智能体的个性化解以适应未知的异构程度，且当各智能体的学习问题足够相似时，能在智能体数量上实现线性提速。我们通过引入PF-LSA算法肯定地回答了该问题，这是一种极简算法，它将每个智能体的局部随机更新与所有智能体的平均更新相结合，且相对于标准联邦方法无额外计算成本。我们证明，PF-LSA无需预先知晓异构程度即可实现两全其美的保证。我们的分析基于将误差精确分解为共识分量与分歧分量：共识误差快速衰减，而分歧误差衰减较慢，但在低异构场景下可忽略不计。
英文摘要
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.
