今天小编就为大家分享一篇Pytorch对Himmelblau函数的优化详解，具有很好的参考价值，希望对大家有所帮助。一起跟随小编过来看看吧
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 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()
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-3 optimizer = 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)=170.0 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
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 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]] #只读取一列 #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 net net_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=0.0001 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)# 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编程之家。
