{"paper":{"title":"On the Linear Speedup of the Push-Pull Method for Decentralized Optimization over Digraphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Gan Luo, Kun Yuan, Liyuan Liang","submitted_at":"2025-06-22T15:41:29Z","abstract_excerpt":"The linear speedup property is essential for demonstrating the advantage of distributed algorithms over their single-node counterparts. In this paper, we study the stochastic Push-Pull method, a widely adopted decentralized optimization algorithm over directed graphs (digraphs). Unlike methods that rely solely on row-stochastic or column-stochastic mixing matrices, Push-Pull avoids nonlinear correction and has shown superior empirical performance across a variety of settings. However, its theoretical analysis remains challenging, and the linear speedup property has not been generally establish"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.18075","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.18075/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}