03.PyTorch深度学习实践——梯度下降

梯度下降（GD）

import matplotlib.pyplot as plt

x_data = [1.0, 2.0, 3.0]
y_data = [2.0, 4.0, 6.0]
w = 1.0


def forward(x):
    return x * w


def cost(xs, ys):
    cost = 0
    for x, y in zip(xs, ys):
        y_pred = forward(x)
        cost += (y_pred - y) ** 2
    return cost / len(xs)


def gradient(xs, ys):
    grad = 0
    for x, y in zip(xs, ys):
        grad += 2 * x * (x * w - y)
    return grad / len(xs)


epoch_list = [i for i in range(1, 101)]
cost_list = []
print('Predict (before training)', 4, forward(4))
for epoch in range(100):
    cost_val = cost(x_data, y_data)
    grad_val = gradient(x_data, y_data)
    w -= 0.01 * grad_val
    cost_list.append(cost_val)
    print('Epoch:', epoch, 'w=', w, 'loss=', cost_val)
print('Predict (after training)', 4, forward(4))

plt.plot(epoch_list, cost_list)
plt.ylabel('cost')
plt.xlabel('epoch')
plt.show()
           

随机梯度下降（SGD）

import matplotlib.pyplot as plt

x_data = [1.0, 2.0, 3.0]
y_data = [2.0, 4.0, 6.0]

w = 1.0


def forward(x):
    return x * w


def loss(x, y):
    y_pred = forward(x)
    return (y_pred - y) ** 2


def gradient(x, y):
    return 2 * x * (x * w - y)


epoch_list = [i for i in range(1, 101)]
loss_list = []
print('Predict (before training)', 4, forward(4))
for epoch in range(100):
    for x, y in zip(x_data, y_data):
        grad = gradient(x, y)
        w = w - 0.01 * grad
        print("\tgrad: ", x, y, grad)
        l = loss(x, y)
    loss_list.append(l)
    print("progress:", epoch, "w=", w, "loss=", l)
print('Predict (after training)', 4, forward(4))

plt.plot(epoch_list, loss_list)
plt.ylabel('loss')
plt.xlabel('epoch')
plt.show()

           

用GD和SGD对比

GD适用于并行计算，计算快；SGD计算慢，但是效果好

所以深度学习的实际使用中常常折中，也就是使用小批量梯度下降

这里的矛盾其实就是batch_size取舍的问题,这在深度学习中是一个难点