PyTorch梯度下降

Question

我正在尝试在PyTorch中手动实现梯度下降作为学习练习。我有以下内容来创建合成数据集：

import torch
torch.manual_seed(0)
N = 100
x = torch.rand(N,1)*5
# Let the following command be the true function
y = 2.3 + 5.1*x
# Get some noisy observations
y_obs = y + 2*torch.randn(N,1)

然后y_pred，如下所示创建我的预测函数（）。

w = torch.randn(1, requires_grad=True)
b = torch.randn(1, requires_grad=True)
y_pred = w*x+b
mse = torch.mean((y_pred-y_obs)**2)

使用MSE推断权重w,b。我使用下面的块根据渐变更新值。

gamma = 1e-2
for i in range(100):
  w = w - gamma *w.grad
  b = b - gamma *b.grad
  mse.backward()

但是，该循环仅在第一次迭代中有效。之后的第二次迭代w.grad设置为None。我相当确定发生这种情况的原因是因为我将w设置为其自身的函数（我可能错了）。

问题是如何使用梯度信息正确地更新权重？

Answer 1

1. 在应用梯度下降之前，您应该调用后向方法。
2. 您需要使用新权重来计算每次迭代的损失。
3. Create new tensor without gradient tape every iteration.

The following code works fine on my computer and gives w=5.1 & b=2.2 after 500 iterations training.

Code:

import torch
torch.manual_seed(0)
N = 100
x = torch.rand(N,1)*5
# Let the following command be the true function
y = 2.3 + 5.1*x
# Get some noisy observations
y_obs = y + 0.2*torch.randn(N,1)

w = torch.randn(1, requires_grad=True)
b = torch.randn(1, requires_grad=True)


gamma = 0.01
for i in range(500):
    print(i)
    # use new weight to calculate loss
    y_pred = w * x + b
    mse = torch.mean((y_pred - y_obs) ** 2)

    # backward
    mse.backward()
    print('w:', w)
    print('b:', b)
    print('w.grad:', w.grad)
    print('b.grad:', b.grad)

    # gradient descent, don't track
    with torch.no_grad():
        w = w - gamma * w.grad
        b = b - gamma * b.grad
    w.requires_grad = True
    b.requires_grad = True

Output:

499
w: tensor([5.1095], requires_grad=True)
b: tensor([2.2474], requires_grad=True)
w.grad: tensor([0.0179])
b.grad: tensor([-0.0576])