---
res:
  bibo_abstract:
  - "LocalSGD and SCAFFOLD are widely used methods in distributed stochastic optimization,
    with numerous applications in machine learning, large-scale data processing, and
    federated learning. However, rigorously establishing their theoretical advantages
    over simpler methods, such as minibatch SGD (MbSGD), has proven challenging, as
    existing analyses often rely on strong assumptions, unrealistic premises, or overly
    restrictive scenarios.\r\n\r\nIn this work, we revisit the convergence properties
    of LocalSGD and SCAFFOLD under a variety of existing or weaker conditions, including
    gradient similarity, Hessian similarity, weak convexity, and Lipschitz continuity
    of the Hessian. Our analysis shows that (i) LocalSGD achieves faster convergence
    compared to MbSGD for weakly convex functions without requiring stronger gradient
    similarity assumptions; (ii) LocalSGD benefits significantly from higher-order
    similarity and smoothness; and (iii) SCAFFOLD demonstrates faster convergence
    than MbSGD for a broader class of non-quadratic functions. These theoretical insights
    provide a clearer understanding of the conditions under which LocalSGD and SCAFFOLD
    outperform MbSGD.@eng"
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Ruichen
      foaf_name: Luo, Ruichen
      foaf_surname: Luo
      foaf_workInfoHomepage: http://www.librecat.org/personId=b391db08-1ffe-11ee-8b67-d18ddcfb5a14
  - foaf_Person:
      foaf_givenName: Sebastian U.
      foaf_name: Stich, Sebastian U.
      foaf_surname: Stich
  - foaf_Person:
      foaf_givenName: Samuel
      foaf_name: Horváth, Samuel
      foaf_surname: Horváth
  - foaf_Person:
      foaf_givenName: Martin
      foaf_name: Takáč, Martin
      foaf_surname: Takáč
  bibo_volume: 258
  dct_date: 2025^xs_gYear
  dct_isPartOf:
  - http://id.crossref.org/issn/2640-3498
  dct_language: eng
  dct_publisher: ML Research Press@
  dct_title: 'Revisiting LocalSGD and SCAFFOLD: Improved rates and missing analysis@'
...