PyTorch梯度下降反向传播

import torch
import matplotlib.pyplot as plt
import os
os.environ["KMP_DUPLICATE_LIB_OK"]  =  "TRUE"
# 数据集
x_data = [1.0,2.0,3.0]
y_data = [2.0,4.0,6.0]
# 权重参数初始值均为1
w = torch.tensor([1.0,1.0,1.0])
w.requires_grad = True    # 需要计算梯度

# 前向传播
def forward(x):
    return w[0]*(x**2)+w[1]*x+w[2]
# 计算损失
def loss(x,y):
    y_pred = forward(x)
    return (y_pred-y) ** 2

# 训练模块
print('predict (before tranining) ',4, forward(4).item())
epoch_list = []
w_list = []
loss_list = []
for epoch in range(1000):
    for x,y in zip(x_data,y_data):
        l = loss(x,y)
        l.backward()        # 后向传播
        print('\tgrad: ',x,y,w.grad.data)
        w.data = w.data - 0.01 * w.grad.data        # 梯度下降
        
        w.grad.data.zero_()    # 梯度清零操作
        
    print('progress: ',epoch,l.item())
    epoch_list.append(epoch)
    w_list.append(w.data)
    loss_list.append(l.item())
print('predict (after tranining) ',4, forward(4).item())

# 绘图
plt.plot(epoch_list,loss_list,'b')
plt.xlabel('Epoch')
plt.ylabel('Loss')
plt.grid()
plt.show()

predict (before tranining)  4 21.0
    grad:  1.0 2.0 tensor([2., 2., 2.])
    grad:  2.0 4.0 tensor([22.8800, 11.4400,  5.7200])
    grad:  3.0 6.0 tensor([77.0472, 25.6824,  8.5608])
progress:  0 18.321826934814453
    grad:  1.0 2.0 tensor([-1.1466, -1.1466, -1.1466])
    grad:  2.0 4.0 tensor([-15.5367,  -7.7683,  -3.8842])
    grad:  3.0 6.0 tensor([-30.4322, -10.1441,  -3.3814])
progress:  1 2.858394145965576
    grad:  1.0 2.0 tensor([0.3451, 0.3451, 0.3451])
    grad:  2.0 4.0 tensor([2.4273, 1.2137, 0.6068])
    grad:  3.0 6.0 tensor([19.4499,  6.4833,  2.1611])
progress:  2 1.1675907373428345
    grad:  1.0 2.0 tensor([-0.3224, -0.3224, -0.3224])
    grad:  2.0 4.0 tensor([-5.8458, -2.9229, -1.4614])
    grad:  3.0 6.0 tensor([-3.8829, -1.2943, -0.4314])
progress:  3 0.04653334245085716
    grad:  1.0 2.0 tensor([0.0137, 0.0137, 0.0137])
    grad:  2.0 4.0 tensor([-1.9141, -0.9570, -0.4785])
    grad:  3.0 6.0 tensor([6.8557, 2.2852, 0.7617])
progress:  4 0.14506366848945618
    grad:  1.0 2.0 tensor([-0.1182, -0.1182, -0.1182])
    grad:  2.0 4.0 tensor([-3.6644, -1.8322, -0.9161])
    grad:  3.0 6.0 tensor([1.7455, 0.5818, 0.1939])
progress:  5 0.009403289295732975
    grad:  1.0 2.0 tensor([-0.0333, -0.0333, -0.0333])
    grad:  2.0 4.0 tensor([-2.7739, -1.3869, -0.6935])
    grad:  3.0 6.0 tensor([4.0140, 1.3380, 0.4460])
progress:  6 0.04972923547029495
    grad:  1.0 2.0 tensor([-0.0501, -0.0501, -0.0501])
    grad:  2.0 4.0 tensor([-3.1150, -1.5575, -0.7788])
    grad:  3.0 6.0 tensor([2.8534, 0.9511, 0.3170])
progress:  7 0.025129113346338272
    grad:  1.0 2.0 tensor([-0.0205, -0.0205, -0.0205])
    grad:  2.0 4.0 tensor([-2.8858, -1.4429, -0.7215])
    grad:  3.0 6.0 tensor([3.2924, 1.0975, 0.3658])
progress:  8 0.03345605731010437
    grad:  1.0 2.0 tensor([-0.0134, -0.0134, -0.0134])
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    grad:  3.0 6.0 tensor([2.9909, 0.9970, 0.3323])
progress:  9 0.027609655633568764
    grad:  1.0 2.0 tensor([0.0033, 0.0033, 0.0033])
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    grad:  3.0 6.0 tensor([3.0377, 1.0126, 0.3375])
progress:  10 0.02848036028444767
    grad:  1.0 2.0 tensor([0.0148, 0.0148, 0.0148])
    grad:  2.0 4.0 tensor([-2.8174, -1.4087, -0.7043])
    grad:  3.0 6.0 tensor([2.9260, 0.9753, 0.3251])
progress:  11 0.02642466314136982
    grad:  1.0 2.0 tensor([0.0280, 0.0280, 0.0280])
    grad:  2.0 4.0 tensor([-2.7682, -1.3841, -0.6920])
    grad:  3.0 6.0 tensor([2.8915, 0.9638, 0.3213])
progress:  12 0.025804826989769936
    grad:  1.0 2.0 tensor([0.0397, 0.0397, 0.0397])
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    grad:  3.0 6.0 tensor([2.8243, 0.9414, 0.3138])
progress:  13 0.02462013065814972
    grad:  1.0 2.0 tensor([0.0514, 0.0514, 0.0514])
    grad:  2.0 4.0 tensor([-2.6934, -1.3467, -0.6734])
    grad:  3.0 6.0 tensor([2.7756, 0.9252, 0.3084])
progress:  14 0.023777369409799576
    grad:  1.0 2.0 tensor([0.0624, 0.0624, 0.0624])
    grad:  2.0 4.0 tensor([-2.6580, -1.3290, -0.6645])
    grad:  3.0 6.0 tensor([2.7213, 0.9071, 0.3024])
progress:  15 0.0228563379496336
    grad:  1.0 2.0 tensor([0.0731, 0.0731, 0.0731])
    grad:  2.0 4.0 tensor([-2.6227, -1.3113, -0.6557])
    grad:  3.0 6.0 tensor([2.6725, 0.8908, 0.2969])
progress:  16 0.022044027224183083
    grad:  1.0 2.0 tensor([0.0833, 0.0833, 0.0833])
    grad:  2.0 4.0 tensor([-2.5893, -1.2946, -0.6473])
    grad:  3.0 6.0 tensor([2.6240, 0.8747, 0.2916])
progress:  17 0.02125072106719017
    grad:  1.0 2.0 tensor([0.0931, 0.0931, 0.0931])
    grad:  2.0 4.0 tensor([-2.5568, -1.2784, -0.6392])
    grad:  3.0 6.0 tensor([2.5780, 0.8593, 0.2864])
progress:  18 0.020513182505965233
    grad:  1.0 2.0 tensor([0.1025, 0.1025, 0.1025])
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    grad:  3.0 6.0 tensor([2.5335, 0.8445, 0.2815])
progress:  19 0.019810274243354797
    grad:  1.0 2.0 tensor([0.1116, 0.1116, 0.1116])
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    grad:  3.0 6.0 tensor([2.4908, 0.8303, 0.2768])
progress:  20 0.019148115068674088
    grad:  1.0 2.0 tensor([0.1203, 0.1203, 0.1203])
    grad:  2.0 4.0 tensor([-2.4669, -1.2335, -0.6167])
    grad:  3.0 6.0 tensor([2.4496, 0.8165, 0.2722])
progress:  21 0.018520694226026535
    grad:  1.0 2.0 tensor([0.1286, 0.1286, 0.1286])
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    grad:  3.0 6.0 tensor([2.4101, 0.8034, 0.2678])
progress:  22 0.017927465960383415
    grad:  1.0 2.0 tensor([0.1367, 0.1367, 0.1367])
    grad:  2.0 4.0 tensor([-2.4124, -1.2062, -0.6031])
    grad:  3.0 6.0 tensor([2.3720, 0.7907, 0.2636])
progress:  23 0.01736525259912014
    grad:  1.0 2.0 tensor([0.1444, 0.1444, 0.1444])
    grad:  2.0 4.0 tensor([-2.3867, -1.1933, -0.5967])
    grad:  3.0 6.0 tensor([2.3354, 0.7785, 0.2595])
progress:  24 0.016833148896694183
    grad:  1.0 2.0 tensor([0.1518, 0.1518, 0.1518])
    grad:  2.0 4.0 tensor([-2.3619, -1.1810, -0.5905])
    grad:  3.0 6.0 tensor([2.3001, 0.7667, 0.2556])
progress:  25 0.01632905937731266
    grad:  1.0 2.0 tensor([0.1589, 0.1589, 0.1589])
    grad:  2.0 4.0 tensor([-2.3380, -1.1690, -0.5845])
    grad:  3.0 6.0 tensor([2.2662, 0.7554, 0.2518])
progress:  26 0.01585075818002224
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    grad:  2.0 4.0 tensor([-2.3151, -1.1575, -0.5788])
    grad:  3.0 6.0 tensor([2.2336, 0.7445, 0.2482])
progress:  27 0.015397666022181511
    grad:  1.0 2.0 tensor([0.1723, 0.1723, 0.1723])
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    grad:  3.0 6.0 tensor([2.2022, 0.7341, 0.2447])
progress:  28 0.014967591501772404
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    grad:  2.0 4.0 tensor([-2.2716, -1.1358, -0.5679])
    grad:  3.0 6.0 tensor([2.1719, 0.7240, 0.2413])
progress:  29 0.014559715054929256
    grad:  1.0 2.0 tensor([0.1846, 0.1846, 0.1846])
    grad:  2.0 4.0 tensor([-2.2511, -1.1255, -0.5628])
    grad:  3.0 6.0 tensor([2.1429, 0.7143, 0.2381])
progress:  30 0.014172340743243694
    grad:  1.0 2.0 tensor([0.1904, 0.1904, 0.1904])
    grad:  2.0 4.0 tensor([-2.2313, -1.1157, -0.5578])
    grad:  3.0 6.0 tensor([2.1149, 0.7050, 0.2350])
progress:  31 0.013804304413497448
    grad:  1.0 2.0 tensor([0.1960, 0.1960, 0.1960])
    grad:  2.0 4.0 tensor([-2.2123, -1.1061, -0.5531])
    grad:  3.0 6.0 tensor([2.0879, 0.6960, 0.2320])
progress:  32 0.013455045409500599
    grad:  1.0 2.0 tensor([0.2014, 0.2014, 0.2014])
    grad:  2.0 4.0 tensor([-2.1939, -1.0970, -0.5485])
    grad:  3.0 6.0 tensor([2.0620, 0.6873, 0.2291])
progress:  33 0.013122711330652237
    grad:  1.0 2.0 tensor([0.2065, 0.2065, 0.2065])
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    grad:  3.0 6.0 tensor([2.0370, 0.6790, 0.2263])
progress:  34 0.01280694268643856
    grad:  1.0 2.0 tensor([0.2114, 0.2114, 0.2114])
    grad:  2.0 4.0 tensor([-2.1592, -1.0796, -0.5398])
    grad:  3.0 6.0 tensor([2.0130, 0.6710, 0.2237])
progress:  35 0.012506747618317604
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progress:  36 0.012220758944749832
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progress:  94 0.006442630663514137
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progress:  95 0.006416172254830599
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progress:  96 0.006390606984496117
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progress:  97 0.0063657015562057495
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progress:  98 0.0063416799530386925
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    grad:  3.0 6.0 tensor([1.4308, 0.4769, 0.1590])
progress:  99 0.00631808303296566
predict (after tranining)  4 8.544171333312988