[
    {
        "id": "osp-16422",
        "type": "article-journal",
        "title": "Best of Both Worlds in Federated LSA: Speedup When Possible, Personalization Always",
        "author": [
            {
                "family": "Labbi",
                "given": "Safwan"
            },
            {
                "family": "Mangold",
                "given": "Paul"
            },
            {
                "family": "Moulines",
                "given": "Eric"
            }
        ],
        "URL": "https://omanscience.com/en/articles/best-of-both-worlds-in-federated-lsa-speedup-when-possible-personalization-always",
        "language": "en",
        "issued": {
            "date-parts": [
                [
                    2026
                ]
            ]
        },
        "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."
    }
]