Stochastic Gradient Descent in Continuous Time: A Central Limit Theorem

Justin Sirignano and Konstantinos Spiliopoulos

Papers from arXiv.org

Abstract: Stochastic gradient descent in continuous time (SGDCT) provides a computationally efficient method for the statistical learning of continuous-time models, which are widely used in science, engineering, and finance. The SGDCT algorithm follows a (noisy) descent direction along a continuous stream of data. The parameter updates occur in continuous time and satisfy a stochastic differential equation. This paper analyzes the asymptotic convergence rate of the SGDCT algorithm by proving a central limit theorem (CLT) for strongly convex objective functions and, under slightly stronger conditions, for non-convex objective functions as well. An $L^{p}$ convergence rate is also proven for the algorithm in the strongly convex case. The mathematical analysis lies at the intersection of stochastic analysis and statistical learning.

Date: 2017-10, Revised 2019-06
New Economics Papers: this item is included in nep-cmp, nep-cta and nep-ecm
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