{"paper":{"title":"Generalization of ERM in Stochastic Convex Optimization: The Dimension Strikes Back","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Vitaly Feldman","submitted_at":"2016-08-15T21:19:51Z","abstract_excerpt":"In stochastic convex optimization the goal is to minimize a convex function $F(x) \\doteq {\\mathbf E}_{{\\mathbf f}\\sim D}[{\\mathbf f}(x)]$ over a convex set $\\cal K \\subset {\\mathbb R}^d$ where $D$ is some unknown distribution and each $f(\\cdot)$ in the support of $D$ is convex over $\\cal K$. The optimization is commonly based on i.i.d.~samples $f^1,f^2,\\ldots,f^n$ from $D$. A standard approach to such problems is empirical risk minimization (ERM) that optimizes $F_S(x) \\doteq \\frac{1}{n}\\sum_{i\\leq n} f^i(x)$. Here we consider the question of how many samples are necessary for ERM to succeed a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.04414","kind":"arxiv","version":3},"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"}