Himmelblau函数如下：

有四个全局最小解，且值都为0，这个函数常用来检验优化算法的表现如何：

可视化函数图像：

import numpy as npfrom matplotlib import pyplot as pltfrom 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()

结果：

使用随机梯度下降优化：

import torch def himmelblau(x): return (x[0] ** 2 + x[1] - 11) ** 2 + (x[0] + x[1] ** 2 - 7) ** 2 # 初始设置为0,0.x = torch.tensor([0., 0.], requires_grad=True)# 优化目标是找到使himmelblau函数值最小的坐标x[0],x[1]，# 也就是x, y# 这里是定义Adam优化器,指明优化目标是x,学习率是1e-3optimizer = torch.optim.Adam([x], lr=1e-3) for step in range(20000): # 每次计算出当前的函数值 pred = himmelblau(x) # 当网络参量进行反馈时,梯度是被积累的而不是被替换掉,这里即每次将梯度设置为0 optimizer.zero_grad() # 生成当前所在点函数值相关的梯度信息,这里即优化目标的梯度信息 pred.backward() # 使用梯度信息更新优化目标的值,即更新x[0]和x[1] optimizer.step() # 每2000次输出一下当前情况 if step % 2000 == 0: print("step={},x={},f(x)={}".format(step, x.tolist(), pred.item()))

输出结果：

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

从上面结果看，找到了一组最优解[3.0, 2.0],此时极小值为0.0。如果修改Tensor变量x的初始化值，可能会找到其它的极小值，也就是说初始化值对于找到最优解很关键。

补充拓展：pytorch 搭建自己的神经网络和各种优化器

还是直接看代码吧！

import torchimport torchvisionimport torchvision.transforms as transformimport torch.utils.data as Dataimport matplotlib.pyplot as pltfrom torch.utils.data import Dataset,DataLoaderimport pandas as pdimport numpy as npfrom torch.autograd import Variable # data settrain=pd.read_csv('Thirdtest.csv')#cut 0 col as labeltrain_label=train.iloc[:,[0]] #只读取一列#train_label=train.iloc[:,0:3]#cut 1~16 col as datatrain_data=train.iloc[:,1:]#change to nptrain_label_np=train_label.valuestrain_data_np=train_data.values #change to tensortrain_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 # 激励函数都在这 class Net(torch.nn.Module): # 继承 torch 的 Module def __init__(self ): super(Net, self).__init__() # 继承 __init__ 功能 self.hidden1 = torch.nn.Linear(16, 30)# 隐藏层线性输出 self.out = torch.nn.Linear(30, 3) # 输出层线性输出 def forward(self, x): # 正向传播输入值, 神经网络分析出输出值 x = F.relu(self.hidden1(x)) # 激励函数(隐藏层的线性值) x = self.out(x) # 输出值, 但是这个不是预测值, 预测值还需要再另外计算 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)) # 为每个优化器创建一个 netnet_SGD = Net()net_Momentum = Net()net_RMSprop = Net()net_Adam = Net()nets = [net_SGD, net_Momentum, net_RMSprop, net_Adam] #定义优化器LR=0.0001opt_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)# 数据必须得是一维非one-hot向量 # 对每个优化器, 优化属于他的神经网络 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)

以上这篇Pytorch对Himmelblau函数的优化详解就是小编分享给大家的全部内容了，希望能给大家一个参考，也希望大家多多支持。