自适应光学系统迭代控制算法超参数优化

Hyper-parameter optimization of iterative control algorithms for adaptive optical systems

无波前探测自适应光学系统中,选择合适的超参数是迭代控制算法达到最佳性能的关键。现有的迭代控制算法的超参数设置一般采用遍历法,这种方法虽然容易理解和实现,但计算量大、耗时较长,同时也可能因为找到一个局部最优值而错过全局最优值。本文采用贝叶斯优化方法,选择适合自适应光学系统迭代控制算法的超参数。分别以常用的随机并行梯度下降算法(stochastic parallel gradient descent algorithm,SPGD)、Momentum-SPGD和CoolMomentum-SPGD控制算法为例,对比分析采用遍历法和贝叶斯优化方法选择超参数的控制算法的校正效果。结果表明,采用贝叶斯优化方法进行超参数选择优势明显。对于SPGD控制算法,取得相同收敛效果时,贝叶斯优化方法所需样本实例数量是遍历法的10%;对于Momentum-SPGD和CoolMomentum-SPGD控制算法,贝叶斯优化方法所需样本实例数量分别是遍历法的7%和9%。研究结果可为自适应光学系统迭代控制算法的实际应用提供超参数设置理论基础。

The selection of suitable hyperparameters in wavefront sensorless adaptive optics systems is the key to achieve the best performance of iterative control algorithms.Existing iterative control algorithms for hyperparameter setting generally use the traversal method,which is easy to understand and implement,but is computationally intensive and time-consuming,and may also miss the global optimum because of finding a local optimum.A Bayesian optimization method was adopted for selecting hyperparameters suitable for iterative control algorithms of adaptive optics systems.The commonly-used stochastic parallel gradient descent algorithm(SPGD),Momentum-SPGD and CoolMomentum-SPGD control algorithms were used as examples to compare and analyze the calibration effects of control algorithms using the traversal method and Bayesian optimization method to select hyperparameters,respectively.The results show that the advantages of using Bayesian optimization method for hyperparameter selection were obvious.For the SPGD control algorithm,the number of sample instances required for the Bayesian optimization method is 10%of that for the traversal method when the same convergence effect is achieved,and for the Momentum-SPGD and CoolMomentum-SPGD control algorithms,the number of sample instances required for the Bayesian optimization method is 7%and 9%of that for the traversal method,respectively.The above findings can provide a theoretical basis for hyperparameter setting in the practical application of iterative control algorithms for adaptive optical systems.