pytorch学习笔记（二）：梯度下降

梯度下降：
w=1.0 a=0.01

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)

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
    print (' Epoch:', epoch, ' w=', w, ' loss=', cost_val)
print ('Predict (after training)', 4 , forward(4))

随机梯度下降：

不求和，改为随机抽取某个样本求导

相当于不往最陡峭的地方下降，而随便往下面走一步

公式对比：

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)

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
        l = loss(x, y)
    print (' Epoch:', epoch, ' w=', w, ' loss=', l)
print ('Predict (after training)', 4 , forward(4))

两者比较
性能：GD<SGD
时间：GD>SGD
因此采用部分（Batch）随机梯度下降（SGD）