【SciPy库】scipy.optimize.fmin_l_bfgs_b进行L-BFGS优化

我就是我 2023-06-28 06:18 3阅读 0赞

【时间】2020.01.07

【题目】【SciPy库】scipy.optimize.fmin\_l\_bfgs\_b进行L-BFGS优化

具体用法参考官方文档：[scipy.optimize.fmin\_l\_bfgs\_b][scipy.optimize.fmin_l_bfgs_b]

x,min_val,info=scipy.optimize.fmin_l_bfgs_b(func, x0, fprime=None, args=(), approx_grad=0, bounds=None, m=10, factr=10000000.0, pgtol=1e-05, epsilon=1e-08, iprint=-1, maxfun=15000, disp=None)

一、参数：主要是loss函数func、待更新参数初始值x0、梯度函数fprime以及maxfun（梯度更新的次数）

**注意grad必须是展开的向量（2D），如果x是3D矩阵，需要先flaten.**

> **func** : callable f(x,\*args)
> 
> Function to minimise.最小化的目标，一般是loss函数
> 
> **x0** : ndarray
> 
> Initial guess.最初的猜测，即待更新参数初始值。
> 
> **fprime** : callable fprime(x,\*args)
> 
> The gradient of *func*. 梯度函数
> 
> If None, then *func* returns the function value and the gradient (f, g = func(x, \*args)), unless *approx\_grad* is True in which case *func* returns only f.
> 
> **args** : sequence
> 
> Arguments to pass to *func* and *fprime*. *func* and *fprime函数的参数*
> 
> **approx\_grad** : bool
> 
> Whether to approximate the gradient numerically (in which case *func* returns only the function value).
> 
> **bounds** : list
> 
> (min, max) pairs for each element in x, defining the bounds on that parameter. Use None for one of min or max when there is no bound in that direction.
> 
> **m** : int
> 
> The maximum number of variable metric corrections used to define the limited memory matrix. (The limited memory BFGS method does not store the full hessian but uses this many terms in an approximation to it.)
> 
> **factr** : float
> 
> The iteration stops when (f^k - f^\{k+1\})/max\{|f^k|,|f^\{k+1\}|,1\} <= factr \* eps, where eps is the machine precision, which is automatically generated by the code. Typical values for *factr* are: 1e12 for low accuracy; 1e7 for moderate accuracy; 10.0 for extremely high accuracy.
> 
> **pgtol** : float
> 
> The iteration will stop when max\{|proj g\_i | i = 1, ..., n\} <= pgtol where pg\_i is the i-th component of the projected gradient.
> 
> **epsilon** : float
> 
> Step size used when *approx\_grad* is True, for numerically calculating the gradient
> 
> **iprint** : int
> 
> Controls the frequency of output. iprint < 0 means no output.
> 
> **disp** : int, optional
> 
> If zero, then no output. If positive number, then this over-rides *iprint*.
> 
> **maxfun** : int
> 
> Maximum number of function evaluations.功能评估的最大数量

二、返回值

> **x** : array\_like
> 
> Estimated position of the minimum.估计最小值的位置，即loss最小时对应的x
> 
> **f** : float
> 
> Value of *func* at the minimum.最小的Func值,即loss值。
> 
> **d** : dict
> 
> Information dictionary.
> 
>  *  d\[‘warnflag’\] is
>     
>      *  0 if converged,
>      *  1 if too many function evaluations,
>      *  2 if stopped for another reason, given in d\[‘task’\]
>  *  d\[‘grad’\] is the gradient at the minimum (should be 0 ish)
>  *  d\[‘funcalls’\] is the number of function calls made. 即梯度更新的次数。

info举例：

{'grad': array([-7.65604162, -2.14013386,  3.16267967, ..., -1.03821039,
           -4.23868084, -3.17428398]),
     'task': b'STOP: TOTAL NO. of f AND g EVALUATIONS EXCEEDS LIMIT', 
    'funcalls': 51, 
    'nit': 47, 'warnflag': 1}

补充：更多scipy库知识：

[Python机器学习及分析工具：Scipy篇][Python_Scipy]

[Scipy lecture note中文文档][Scipy lecture note]

[scipy.optimize.fmin_l_bfgs_b]: https://docs.scipy.org/doc/scipy-0.10.1/reference/generated/scipy.optimize.fmin_l_bfgs_b.html
[Python_Scipy]: https://www.jianshu.com/p/6c742912047f
[Scipy lecture note]: https://wizardforcel.gitbooks.io/scipy-lecture-notes/content/4.html