中国激光, 2014, 41 (7): 0712001, 网络出版: 2014-04-29
基于分段随机扰动幅值的随机并行梯度下降算法研究
Research of Stochastic Parallel Gradient Descent Algorithm Based on Segmentation Random Disturbance Amplitude
自适应光学 波前校正 随机并行梯度下降 分段随机扰动幅值 adaptive optics wavefront correction stochastic parallel gradient descent segmentation random perturbance amplitude
摘要
为了提高随机并行梯度下降(SPGD)算法的收敛速度,提出了分段随机扰动幅值的改进方法。从理论上分析了固定增益系数时,随机扰动幅值对SPGD 算法收敛速度的影响;提出了分段随机扰动幅值的改进方法;基于61单元变形镜,建立无波前探测自适应光学系统模型,对前65阶Zernike多项式模拟的满足Kolmogorov谱的大气湍流畸变波前进行校正。结果表明,采用分段随机扰动幅值的SPGD算法比固定最佳随机扰动幅值时传统SPGD算法的收敛速度提高了近1.6倍,证明了该改进算法的可行性。
Abstract
The improved method of random perturbance amplitude section is proposed to increase the convergence speed of stochastic parallel gradient descent (SPGD) algorithm. The SPGD algorithm convergence rate, which can be effected by the random disturbance amplitude, is analyzed when the gain coefficient is fixed. The segmentation random perturbance amplitude method is put forward. The adaptive optics system without wavefront sensor is built with a 61-element deformation mirror to correct the wavefront aberrations, which is simulated by the 65-order Zernike polynomials and the aberrations meet the Kolmogorov spectrum. Compared with the best fixed initial perturbance amplitude SPGD algorithm, the convergence speed increases 1.6 times by adopting the SPGD algorithm based on the segmentation random perturbance amplitude. The improved algorithm is verified to be feasible.
吴健, 杨慧珍, 龚成龙. 基于分段随机扰动幅值的随机并行梯度下降算法研究[J]. 中国激光, 2014, 41(7): 0712001. Wu Jian, Yang Huizhen, Gong Chenglong. Research of Stochastic Parallel Gradient Descent Algorithm Based on Segmentation Random Disturbance Amplitude[J]. Chinese Journal of Lasers, 2014, 41(7): 0712001.