同构与异构异步优化之间的差距为何难以弥合

Mathematics > Optimization and Control arXiv:2609.17483v1 (math) [Submitted on 15 Sep 2026] Title:Bridging the Gap Between Homogeneous and Heterogeneous Asynchronous Optimization Is Surprisingly Difficult Authors:Alexander Tyurin View a PDF of the paper titled Bridging the Gap Between Homogeneous and Heterogeneous Asynchronous Optimization Is Surprisingly Difficult, by Alexander Tyurin View PDF HTML (experimental) Abstract:Modern large-scale machine learning tasks often require multiple workers, devices, CPUs, or GPUs to compute stochastic gradients in parallel and asynchronously to train model weights. Theoretical results typically distinguish between two settings: (i) the homogeneous setting, where all workers have access to the same data distribution, and (ii) the heterogeneous setting, where each worker operates on different data distributions. Known optimal time complexities in these settings reveal a significant gap, with far more pessimistic guarantees in the heterogeneous case. In this work, we investigate whether these pessimistic optimal time complexities can be overcome under different assumptions. Surprisingly, we show that improvement is provably impossible under widely used first- and second-order similarity assumptions for any randomized algorithm. We then turn to the interpolation regime and demonstrate that the weak interpolation assumption alone is also insufficient. Finally, we introduce a minimal combination of irreducible assumptions, strong interpolation and the local Polyak-Lojasiewicz condition, to derive a new time complexity bound that matches the dependence on worker computation times in the best-known result in the homogeneous setting, without requiring identical data distributions. Subjects: Optimization and Control (math.OC); Machine Learning (cs.LG) Cite as: arXiv:2609.17483 [math.OC] (or arXiv:2609.17483v1 [math.OC] for this version) https://doi.org/10.48550/arXiv.2609.17483 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Alexander Tyurin [view email] [v1] Tue, 15 Sep 2026 17:24:09 UTC (303 KB) Full-text links: Access Paper: View a PDF of the paper titled Bridging the Gap Between Homogeneous and Heterogeneous Asynchronous Optimization Is Surprisingly Difficult, by Alexander Tyurin View PDF HTML (experimental) TeX Source view license Current browse context: math.OC new | recent | 2026-09 Change to browse by: cs cs.LG math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)