比较不同的优化器

比较不同的优化器

以下代码比较了神经网络不同优化器的收敛速度：

import torch
import torch.utils.data as Data
import torch.nn.functional as F
from torch.autograd import Variable
import matplotlib.pyplot as plt

if __name__ == '__main__':

    # hyper parameters
    LR = 0.01
    BATCH_SIZE = 32
    EPOCH = 12

    x = torch.unsqueeze(torch.linspace(-1, 1, 1000), dim=1)
    y = x.pow(2) + 0.1 * torch.normal(torch.zeros(*x.size()))
    # torch.zeros(size): a tensor of size,filled by 0
    # torch.normal(mean): a random number of mean

    torch_dataset = Data.TensorDataset(x, y)
    loader = Data.DataLoader(dataset=torch_dataset, batch_size=BATCH_SIZE, shuffle=True, num_workers=2)


    class Net(torch.nn.Module):
        def __init__(self):
            super(Net, self).__init__()
            self.hidden = torch.nn.Linear(1, 20)  # hidden layer
            self.predict = torch.nn.Linear(20, 1)  # output layer

        def forward(self, x):
            x = F.relu(self.hidden(x))  # relu is activation function between hidden and predict
            x = self.predict(x)
            return x


    # 4 nets of same structure
    net_SGD = Net()
    net_Momentum = Net()
    net_RMSprop = Net()
    net_Adam = Net()

    nets = [net_SGD, net_Momentum, net_RMSprop, net_Adam]  # together

    # 4 nets of same structure but 4 different optimizers
    opt_SGD = torch.optim.SGD(net_SGD.parameters(), lr=LR)
    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.MSELoss()
    loss_his = [[], [], [], []]

    for epoch in range(EPOCH):
        print(epoch)
        for step, (batch_x, batch_y) in enumerate(loader):

            # turn to variable to be put into the net
            b_x = Variable(batch_x)
            b_y = Variable(batch_y)

            for net, opt, l_his in zip(nets, optimizers, loss_his):
                output = net(b_x)  # output of net
                loss = loss_func(output, b_y)  # loss of net
                opt.zero_grad()  # clear gradients for next train
                loss.backward()  # back propagation,compute gradients
                opt.step()  # apply gradients
                l_his.append(loss.data)  # record loss

    labels = ['SGD', 'Momentum', 'RMSprop', 'Adam']
    for i, l_his in enumerate(loss_his):
        plt.plot(l_his, label=labels[i])  # label:what the line is
    plt.legend(loc='best')  # set the label to the 'best' place
    plt.xlabel('Steps')
    plt.ylabel('Loss')
    plt.ylim((0, 0.2))
    plt.show()

输出结果：

结果图的纵坐标是误差，横坐标是训练批数，优化器最终目标是误差接近零，接近零的过程叫收敛，越快收敛越好。

SGD作为最基础的优化器收敛最慢。

Momentum在梯度下降时增加斜坡，使下降速度变快。

AdaGrad在梯度下降时，减少左右摆动，使梯度方向保持直线。图中未画出此方法。

RMSprop结合了Momentum与AdaGrad的优点，反应在图上是最快的收敛速度。

Adam是RMSprop的升级版，不仅拥有最快的收敛速度，而且与RMSprop误差波动不大。