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In this article, we first investigate the global optimizing objective in FL and demonstrate that, due to data heterogeneity and partial client participation, the global updates in a single training epoch may diverge from the intended objectives of conventional FL methods. To address this problem, we introduce a triple-objective decomposition mechanism to decompose the overarching global objective into three distinct local objectives aimed at aligning client gradients. Subsequently, we propose a gradient trajectory smoothing technique known as FedGTS, which refines local updates by estimating a pseudo-gradient leveraging historical global update trajectories. This approach is designed to mitigate performance oscillations and enhance the stability of the learning process. We theoretically demonstrate that our approach reduces variance of local updates and achieves a guaranteed convergence rate. We experimentally show that the proposed method outperforms the baselines with faster convergence and higher accuracy. Extensive experiments validate the effectiveness of the proposed approach across various heterogeneity settings. Our codes are publicly available at GitHub (\n            <jats:ext-link xmlns:xlink=\"https:\/\/2.zoppoz.workers.dev:443\/http\/www.w3.org\/1999\/xlink\" ext-link-type=\"uri\" xlink:href=\"https:\/\/2.zoppoz.workers.dev:443\/https\/github.com\/ZongHR\/FedGTS\">https:\/\/2.zoppoz.workers.dev:443\/https\/github.com\/ZongHR\/FedGTS<\/jats:ext-link>\n            ).\n          <\/jats:p>","DOI":"10.1145\/3743142","type":"journal-article","created":{"date-parts":[[2025,6,6]],"date-time":"2025-06-06T11:53:12Z","timestamp":1749210792000},"page":"1-31","update-policy":"https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":1,"title":["Convergence-Guaranteed Federated Learning through Gradient Trajectory Smoothing with Triple-Objective Decomposition"],"prefix":"10.1145","volume":"19","author":[{"ORCID":"https:\/\/2.zoppoz.workers.dev:443\/https\/orcid.org\/0009-0000-7514-9019","authenticated-orcid":false,"given":"Haoran","family":"Zong","sequence":"first","affiliation":[{"name":"State Key Laboratory for Novel Software Technology, Nanjing University, Nanjing, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/2.zoppoz.workers.dev:443\/https\/orcid.org\/0000-0003-0824-9284","authenticated-orcid":false,"given":"Xiao","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Computer Science and Technology, Shandong University, Jinan, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/2.zoppoz.workers.dev:443\/https\/orcid.org\/0009-0004-3900-679X","authenticated-orcid":false,"given":"Ruichen","family":"Li","sequence":"additional","affiliation":[{"name":"State Key Laboratory for Novel Software Technology, Nanjing University, Nanjing, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/2.zoppoz.workers.dev:443\/https\/orcid.org\/0000-0002-2492-609X","authenticated-orcid":false,"given":"Jianhui","family":"Duan","sequence":"additional","affiliation":[{"name":"State Key Laboratory for Novel Software Technology, Nanjing University, Nanjing, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/2.zoppoz.workers.dev:443\/https\/orcid.org\/0009-0008-2186-5931","authenticated-orcid":false,"given":"Derun","family":"Zou","sequence":"additional","affiliation":[{"name":"State Key Laboratory for Novel Software Technology, Nanjing University, Nanjing, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/2.zoppoz.workers.dev:443\/https\/orcid.org\/0000-0002-9199-3655","authenticated-orcid":false,"given":"Wenzhong","family":"Li","sequence":"additional","affiliation":[{"name":"State Key Laboratory for Novel Software Technology, Nanjing University, Nanjing, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2025,8,7]]},"reference":[{"key":"e_1_3_1_2_2","unstructured":"Durmus Alp Emre Acar Yue Zhao Ramon Matas Navarro Matthew Mattina Paul N. 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