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Pytorch對(duì)Himmelblau函數(shù)的優(yōu)化詳解

更新時(shí)間：2020年02月29日 11:17:27 作者：洪流之源

今天小編就為大家分享一篇Pytorch對(duì)Himmelblau函數(shù)的優(yōu)化詳解，具有很好的參考價(jià)值，希望對(duì)大家有所幫助。一起跟隨小編過來(lái)看看吧

Himmelblau函數(shù)如下：

有四個(gè)全局最小解，且值都為0，這個(gè)函數(shù)常用來(lái)檢驗(yàn)優(yōu)化算法的表現(xiàn)如何：

可視化函數(shù)圖像：

import numpy as np
from matplotlib import pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
 
def himmelblau(x):
 return (x[0] ** 2 + x[1] - 11) ** 2 + (x[0] + x[1] ** 2 - 7) ** 2
 
x = np.arange(-6, 6, 0.1)
y = np.arange(-6, 6, 0.1)
X, Y = np.meshgrid(x, y)
Z = himmelblau([X, Y])
fig = plt.figure("himmeblau")
ax = fig.gca(projection='3d')
ax.plot_surface(X, Y, Z)
ax.view_init(60, -30)
ax.set_xlabel('x')
ax.set_ylabel('y')
plt.show()

結(jié)果：

使用隨機(jī)梯度下降優(yōu)化：

import torch
 
 def himmelblau(x):
 return (x[0] ** 2 + x[1] - 11) ** 2 + (x[0] + x[1] ** 2 - 7) ** 2
 
# 初始設(shè)置為0,0.
x = torch.tensor([0., 0.], requires_grad=True)
# 優(yōu)化目標(biāo)是找到使himmelblau函數(shù)值最小的坐標(biāo)x[0],x[1]，
# 也就是x, y
# 這里是定義Adam優(yōu)化器,指明優(yōu)化目標(biāo)是x,學(xué)習(xí)率是1e-3
optimizer = torch.optim.Adam([x], lr=1e-3)
 
for step in range(20000):
 # 每次計(jì)算出當(dāng)前的函數(shù)值
 pred = himmelblau(x)
 # 當(dāng)網(wǎng)絡(luò)參量進(jìn)行反饋時(shí),梯度是被積累的而不是被替換掉,這里即每次將梯度設(shè)置為0
 optimizer.zero_grad()
 # 生成當(dāng)前所在點(diǎn)函數(shù)值相關(guān)的梯度信息,這里即優(yōu)化目標(biāo)的梯度信息
 pred.backward()
 # 使用梯度信息更新優(yōu)化目標(biāo)的值,即更新x[0]和x[1]
 optimizer.step()
 # 每2000次輸出一下當(dāng)前情況
 if step % 2000 == 0:
 print("step={},x={},f(x)={}".format(step, x.tolist(), pred.item()))

輸出結(jié)果：

step=0,x=[0.0009999999310821295, 0.0009999999310821295],f(x)=170.0
step=2000,x=[2.3331806659698486, 1.9540692567825317],f(x)=13.730920791625977
step=4000,x=[2.9820079803466797, 2.0270984172821045],f(x)=0.014858869835734367
step=6000,x=[2.999983549118042, 2.0000221729278564],f(x)=1.1074007488787174e-08
step=8000,x=[2.9999938011169434, 2.0000083446502686],f(x)=1.5572823031106964e-09
step=10000,x=[2.999997854232788, 2.000002861022949],f(x)=1.8189894035458565e-10
step=12000,x=[2.9999992847442627, 2.0000009536743164],f(x)=1.6370904631912708e-11
step=14000,x=[2.999999761581421, 2.000000238418579],f(x)=1.8189894035458565e-12
step=16000,x=[3.0, 2.0],f(x)=0.0
step=18000,x=[3.0, 2.0],f(x)=0.0

從上面結(jié)果看，找到了一組最優(yōu)解[3.0, 2.0],此時(shí)極小值為0.0。如果修改Tensor變量x的初始化值，可能會(huì)找到其它的極小值，也就是說(shuō)初始化值對(duì)于找到最優(yōu)解很關(guān)鍵。

補(bǔ)充拓展：pytorch 搭建自己的神經(jīng)網(wǎng)絡(luò)和各種優(yōu)化器

還是直接看代碼吧！

import torch
import torchvision
import torchvision.transforms as transform
import torch.utils.data as Data
import matplotlib.pyplot as plt
from torch.utils.data import Dataset,DataLoader
import pandas as pd
import numpy as np
from torch.autograd import Variable
 
# data set
train=pd.read_csv('Thirdtest.csv')
#cut 0 col as label
train_label=train.iloc[:,[0]] #只讀取一列
#train_label=train.iloc[:,0:3]
#cut 1~16 col as data
train_data=train.iloc[:,1:]
#change to np
train_label_np=train_label.values
train_data_np=train_data.values
 
#change to tensor
train_label_ts=torch.from_numpy(train_label_np)
train_data_ts=torch.from_numpy(train_data_np)
 
train_label_ts=train_label_ts.type(torch.LongTensor)
train_data_ts=train_data_ts.type(torch.FloatTensor)
 
 
 
print(train_label_ts.shape)
print(type(train_label_ts))
 
train_dataset=Data.TensorDataset(train_data_ts,train_label_ts)
train_loader=DataLoader(dataset=train_dataset,batch_size=64,shuffle=True)
 
#make a network
 
import torch.nn.functional as F   # 激勵(lì)函數(shù)都在這
 
class Net(torch.nn.Module):   # 繼承 torch 的 Module
  def __init__(self ):
    super(Net, self).__init__()   # 繼承 __init__ 功能
    self.hidden1 = torch.nn.Linear(16, 30)# 隱藏層線性輸出
    self.out = torch.nn.Linear(30, 3)    # 輸出層線性輸出
 
  def forward(self, x):
    # 正向傳播輸入值, 神經(jīng)網(wǎng)絡(luò)分析出輸出值
    x = F.relu(self.hidden1(x))   # 激勵(lì)函數(shù)(隱藏層的線性值)
    x = self.out(x)         # 輸出值, 但是這個(gè)不是預(yù)測(cè)值, 預(yù)測(cè)值還需要再另外計(jì)算
    return x
 
 
# net=Net()
# optimizer = torch.optim.SGD(net.parameters(), lr=0.0001,momentum=0.001)
# loss_func = torch.nn.CrossEntropyLoss() # the target label is NOT an one-hotted
 
# loss_list=[]
# for epoch in range(500):
#   for step ,(b_x,b_y) in enumerate (train_loader):
#     b_x,b_y=Variable(b_x),Variable(b_y)
#     b_y=b_y.squeeze(1)
#     output=net(b_x)
#     loss=loss_func(output,b_y)
#     optimizer.zero_grad()
#     loss.backward()
#     optimizer.step()
#     if epoch%1==0:
#       loss_list.append(float(loss))
#     print( "Epoch: ", epoch, "Step ", step, "loss: ", float(loss))
 
 
# 為每個(gè)優(yōu)化器創(chuàng)建一個(gè) net
net_SGD     = Net()
net_Momentum  = Net()
net_RMSprop   = Net()
net_Adam    = Net()
nets = [net_SGD, net_Momentum, net_RMSprop, net_Adam]
 
#定義優(yōu)化器
LR=0.0001
opt_SGD     = torch.optim.SGD(net_SGD.parameters(), lr=LR,momentum=0.001)
opt_Momentum  = torch.optim.SGD(net_Momentum.parameters(), lr=LR, momentum=0.8)
opt_RMSprop   = torch.optim.RMSprop(net_RMSprop.parameters(), lr=LR, alpha=0.9)
opt_Adam    = torch.optim.Adam(net_Adam.parameters(), lr=LR, betas=(0.9, 0.99))
optimizers = [opt_SGD, opt_Momentum, opt_RMSprop, opt_Adam]
 
loss_func = torch.nn.CrossEntropyLoss()
losses_his = [[], [], [], []]
 
for net, opt, l_his in zip(nets, optimizers, losses_his):
  for epoch in range(500):
    for step, (b_x, b_y) in enumerate(train_loader):
      b_x, b_y = Variable(b_x), Variable(b_y)
      b_y = b_y.squeeze(1)# 數(shù)據(jù)必須得是一維非one-hot向量
    # 對(duì)每個(gè)優(yōu)化器, 優(yōu)化屬于他的神經(jīng)網(wǎng)絡(luò)
 
      output = net(b_x)       # get output for every net
      loss = loss_func(output, b_y) # compute loss for every net
      opt.zero_grad()        # clear gradients for next train
      loss.backward()        # backpropagation, compute gradients
      opt.step()           # apply gradients
      if epoch%1==0:
        l_his.append(loss.data.numpy())   # loss recoder
        print("optimizers: ",opt,"Epoch: ",epoch,"Step ",step,"loss: ",float(loss))
 
labels = ['SGD', 'Momentum', 'RMSprop', 'Adam']
for i, l_his in enumerate(losses_his):
  plt.plot(l_his, label=labels[i])
plt.legend(loc='best')
plt.xlabel('Steps')
plt.ylabel('Loss')
plt.xlim((0,1000))
plt.ylim((0,4))
plt.show()
 

 
#
# for epoch in range(5):
#   for step ,(b_x,b_y) in enumerate (train_loader):
#     b_x,b_y=Variable(b_x),Variable(b_y)
#     b_y=b_y.squeeze(1)
#     output=net(b_x)
#     loss=loss_func(output,b_y)
#     loss.backward()
#     optimizer.zero_grad()
#     optimizer.step()
#     print(loss)

以上這篇Pytorch對(duì)Himmelblau函數(shù)的優(yōu)化詳解就是小編分享給大家的全部?jī)?nèi)容了，希望能給大家一個(gè)參考，也希望大家多多支持腳本之家。

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