Web: http://arxiv.org/abs/2201.08518

Jan. 24, 2022, 2:10 a.m. | Wenlong Mou, Koulik Khamaru, Martin J. Wainwright, Peter L. Bartlett, Michael I. Jordan

cs.LG updates on arXiv.org arxiv.org

We study the problem of estimating the fixed point of a contractive operator
defined on a separable Banach space. Focusing on a stochastic query model that
provides noisy evaluations of the operator, we analyze a variance-reduced
stochastic approximation scheme, and establish non-asymptotic bounds for both
the operator defect and the estimation error, measured in an arbitrary
semi-norm. In contrast to worst-case guarantees, our bounds are
instance-dependent, and achieve the local asymptotic minimax risk
non-asymptotically. For linear operators, contractivity can be …

arxiv math stochastic variance

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