{"paper":{"title":"Computational Optimal Transport: Complexity by Accelerated Gradient Descent Is Better Than by Sinkhorn's Algorithm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.DS","authors_text":"Alexander Gasnikov, Alexey Kroshnin, Pavel Dvurechensky","submitted_at":"2018-02-12T21:33:39Z","abstract_excerpt":"We analyze two algorithms for approximating the general optimal transport (OT) distance between two discrete distributions of size $n$, up to accuracy $\\varepsilon$. For the first algorithm, which is based on the celebrated Sinkhorn's algorithm, we prove the complexity bound $\\widetilde{O}\\left({n^2/\\varepsilon^2}\\right)$ arithmetic operations. For the second one, which is based on our novel Adaptive Primal-Dual Accelerated Gradient Descent (APDAGD) algorithm, we prove the complexity bound $\\widetilde{O}\\left(\\min\\left\\{n^{9/4}/\\varepsilon, n^{2}/\\varepsilon^2 \\right\\}\\right)$ arithmetic opera"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.04367","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}