{"paper":{"title":"A Communication Complexity Lower Bound for Nonuniformly Convex Consensus Optimization","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DC"],"primary_cat":"math.OC","authors_text":"Demyan Yarmoshik, Maxim Klimenko","submitted_at":"2026-06-10T21:01:24Z","abstract_excerpt":"We study the communication complexity of convex decentralized optimization over time-varying networks, where $n$ nodes hold private functions and must agree on the global minimizer using only synchronous exchanges with neighbors. The cost is the number of communication rounds to reach accuracy $\\varepsilon$ -- a measure akin to round complexity in the LOCAL model, but constrained by nodes sharing only oracle responses. We prove a new lower bound of $\\Omega\\!\\left(\\chi_{\\mathcal G} \\sqrt{\\kappa_g}\\,\\log\\frac{n}{\\chi_{\\mathcal G}}\\log\\frac1\\varepsilon\\right)$ communication rounds, where $\\chi_{\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.12675","kind":"arxiv","version":1},"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/2606.12675/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"}