Stochastic Gradient Descent in Continuous Time
Stochastic Gradient Descent in Continuous Time
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DOI：
10.2139/ssrn.2954149
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发表时间：
2016-11
期刊：
影响因子：
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通讯作者：
Justin A. Sirignano;K. Spiliopoulos
中科院分区：
文献类型：
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作者：
Justin A. Sirignano;K. Spiliopoulos
连续时间随机梯度下降(SGDCT)为连续时间模型的统计学习提供了一种高效的计算方法，这些模型广泛应用于科学、工程和金融等领域。SGDCT算法沿着连续的数据流沿着(有噪声的)下降方向。SGDCT连续进行参数在线更新，参数更新满足随机微分方程式。我们证明了$lim_{t\right tarrow\inty}\nabla_g(\theta_t)=0$，其中$\bar g$是估计连续时间动态的自然目标函数。收敛证明利用遍历性，使用适当的泊松方程来帮助描述参数在大时间内的演化。对于某些连续时间问题，SGDCT与传统的随机梯度下降算法相比具有一些很有前途的优势。本文主要研究了模型估计在金融领域的应用，如股票、债券、利率等的模型估计。
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 ...