{"paper":{"title":"Finite-sum Composition Optimization via Variance Reduced Gradient Descent","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Ji Liu, Mengdi Wang, Xiangru Lian","submitted_at":"2016-10-15T00:27:21Z","abstract_excerpt":"The stochastic composition optimization proposed recently by Wang et al. [2014] minimizes the objective with the compositional expectation form: $\\min_x~(\\mathbb{E}_iF_i \\circ \\mathbb{E}_j G_j)(x).$ It summarizes many important applications in machine learning, statistics, and finance. In this paper, we consider the finite-sum scenario for composition optimization: \\[\\min_x f (x) := \\frac{1}{n} \\sum_{i = 1}^n F_i \\left(\\frac{1}{m} \\sum_{j = 1}^m G_j (x) \\right). \\] We propose two algorithms to solve this problem by combining the stochastic compositional gradient descent (SCGD) and the stochast"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.04674","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":""},"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"}