{"paper":{"title":"Solving Empirical Risk Minimization in the Current Matrix Multiplication Time","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["cs.LG","math.OC","stat.ML"],"primary_cat":"cs.DS","authors_text":"Qiuyi Zhang, Yin Tat Lee, Zhao Song","submitted_at":"2019-05-11T04:42:16Z","abstract_excerpt":"Many convex problems in machine learning and computer science share the same form: \\begin{align*} \\min_{x} \\sum_{i} f_i( A_i x + b_i), \\end{align*} where $f_i$ are convex functions on $\\mathbb{R}^{n_i}$ with constant $n_i$, $A_i \\in \\mathbb{R}^{n_i \\times d}$, $b_i \\in \\mathbb{R}^{n_i}$ and $\\sum_i n_i = n$. This problem generalizes linear programming and includes many problems in empirical risk minimization. In this paper, we give an algorithm that runs in time \\begin{align*} O^* ( ( n^{\\omega} + n^{2.5 - \\alpha/2} + n^{2+ 1/6} ) \\log (n / \\delta) ) \\end{align*} where $\\omega$ is the exponent"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.04447","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":""},"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"}