Stochastic Gradient Descent in Continuous Time: A Central Limit Theorem

Justin Sirignano; Konstantinos Spiliopoulos

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arXiv · 1710.04273

Stochastic Gradient Descent in Continuous Time: A Central Limit Theorem

Justin Sirignano·Konstantinos Spiliopoulos

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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.

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BibTeX RIS

Justin Sirignano, Konstantinos Spiliopoulos. 2017-10-11. Stochastic Gradient Descent in Continuous Time: A Central Limit Theorem. https://arxiv.org/abs/1710.04273

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