May 21, 2024, 4:44 a.m. | Hongcheng Liu, Jindong Tong

cs.LG updates on arXiv.org arxiv.org

arXiv:2401.00664v2 Announce Type: replace-cross
Abstract: This paper studies the sample average approximation (SAA) in solving convex or strongly convex stochastic programming problems. Under some common regularity conditions, we show -- perhaps for the first time -- that the SAA's sample complexity can be completely free from any quantification of metric entropy (such as the logarithm of the covering number), leading to a significantly more efficient rate with dimensionality $d$ than most existing results. From the newly established complexity bounds, an …

abstract approximation arxiv complexity cs.lg entropy free math.oc math.pr math.st paper programming replace sample show stat.th stochastic studies type

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