Stochastic Gradient Descent in Continuous Time

By Justin A. Sirignano, Konstantinos Spiliopoulos. 2016

68 citations recorded by the source corpus.

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. SGDCT performs an online parameter update in continuous time with the parameter updates $\theta_t$ satisfying a stochastic differential equation. We prove that $\lim_{t \rightarrow \infty} \nabla \bar g(\theta_t) = 0$, where $\bar g$ is a natural objective function for the estimation of the continuous-time dynamics. The convergence proof leverages ergodicity by using an appropriate Poisson equation to help describe the evolution of the parameters for large times. For certain continuous-time problems, SGDCT has some promising advantages compared to a traditional stochastic gradient descent algorithm. This paper mainly focuses on applications in finance, such as model estimation for stocks, bonds, interest ...

Subfields: Finance, Ocean Engineering, Statistics and Probability

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Citations in the corpus

Universal features of price formation in financial markets: perspectives from deep learning (2018, methodology): “This is one of the reasons why, except in a few instances [7, 14, 25, 28, 29, 30], large-scale learning methods such as Deep Learning [18] have not been deployed for quantitative modeling in finance.”
Mean Field Analysis of Neural Networks: A Law of Large Numbers (2018, background): “Han, Jentzen and E (2017), Sirignano and Spiliopoulos (2016,2017), Jentzen et all (2018) Konstantinos Spiliopoulos ( Department of Mathematics & Statistics, Boston University Partially supported by career award NSF-DMS 1550918 Joint work with Justin Sirignano (University of Illinois at Urbana-Champa”
DGM: A deep learning algorithm for solving partial differential equations (2017, neutral): “1 r + d 2q = 1 q ∈ (d/2,∞], r ∈ [1,∞), for d ≥ 2, q ∈ [1,∞], r ∈ [1, 2], for d = 1.”
Deep learning for limit order books (2016, unknown): “Sirignano and Spiliopoulos (2017a) and Sirignano and Spiliopoulos (2017b) use machine learning to estimate stochastic differential equation models.”
Mean Field Analysis of Deep Neural Networks (2019, background): “[60]), and text recognition (see [62] and [57]). Neural networks also nd increasing more applications in engineering, robotics, medicine, and nance (see [37], [38], [58], [26], [47], [3], [51], [52], [53], and [54]). In this paper we characterize multi-layer neural networks in the asymptotic regime ”