一种快速收敛的随机并行梯度下降算法

Fast Convergence Stochastic Parallel Gradient Descent Algorithm

理论模拟仿真了基于变形镜与随机并行梯度下降(SPGD)算法的无波前探测自适应光学系统(AOS)。为提高基于SPGD算法的无波前探测AOS的收敛速度,在不降低精度的前提下,对SPGD算法中关键参数随机扰动幅值和增益系数的关系进行了优化。实验发现,AOS存在参数优选区域,且与初始畸变大小有关。进行了理论验证并与模拟退火算法进行了比较,结果表明,SPGD算法收敛精度比模拟退火算法高6.32%,具有更好的收敛速度。

In this paper,based on deformable mirrors and the stochastic parallel-gradient-descent(SPGD)algorithm,an adaptive optics system(AOS)without wavefront detection is theoretically simulated.In order to improve the convergence speed of the AOS without reducing its accuracy,this paper optimizes the relationship between the amplitude of random perturbation and the gain coefficient in the SPGD algorithm.The experiment conducted in this study shows that the AOS has a parameter preference area,which is related to the initial distortion magnitude.Furthermore,the results of the theoretical verification and the comparison with that by the simulated annealing algorithm reveal that the convergence accuracy of the SPGD algorithm is 6.32%higher than that of the SA algorithm and the SPGD algorithm has a larger convergence speed.