pytorch 實現(xiàn)L2和L1正則化regularization的操作

更新時間：2021年03月03日 10:44:41 作者：pan_jinquan

這篇文章主要介紹了pytorch 實現(xiàn)L2和L1正則化regularization的操作，具有很好的參考價值，希望對大家有所幫助。一起跟隨小編過來看看吧

1.torch.optim優(yōu)化器實現(xiàn)L2正則化

torch.optim集成了很多優(yōu)化器，如SGD，Adadelta，Adam，Adagrad，RMSprop等，這些優(yōu)化器自帶的一個參數(shù)weight_decay，用于指定權(quán)值衰減率，相當于L2正則化中的λ參數(shù)，注意torch.optim集成的優(yōu)化器只有L2正則化方法，你可以查看注釋，參數(shù)weight_decay 的解析是：

weight_decay (float, optional): weight decay (L2 penalty) (default: 0)

使用torch.optim的優(yōu)化器，可如下設置L2正則化

optimizer = optim.Adam(model.parameters(),lr=learning_rate,weight_decay=0.01)

但是這種方法存在幾個問題，

（1）一般正則化，只是對模型的權(quán)重W參數(shù)進行懲罰，而偏置參數(shù)b是不進行懲罰的，而torch.optim的優(yōu)化器weight_decay參數(shù)指定的權(quán)值衰減是對網(wǎng)絡中的所有參數(shù)，包括權(quán)值w和偏置b同時進行懲罰。很多時候如果對b 進行L2正則化將會導致嚴重的欠擬合，因此這個時候一般只需要對權(quán)值w進行正則即可。（PS：這個我真不確定，源碼解析是 weight decay (L2 penalty) ，但有些網(wǎng)友說這種方法會對參數(shù)偏置b也進行懲罰，可解惑的網(wǎng)友給個明確的答復）

（2）缺點：torch.optim的優(yōu)化器固定實現(xiàn)L2正則化，不能實現(xiàn)L1正則化。如果需要L1正則化，可如下實現(xiàn)：

（3）根據(jù)正則化的公式，加入正則化后，loss會變原來大，比如weight_decay=1的loss為10，那么weight_decay=100時，loss輸出應該也提高100倍左右。而采用torch.optim的優(yōu)化器的方法，如果你依然采用loss_fun= nn.CrossEntropyLoss()進行計算loss，你會發(fā)現(xiàn)，不管你怎么改變weight_decay的大小，loss會跟之前沒有加正則化的大小差不多。這是因為你的loss_fun損失函數(shù)沒有把權(quán)重W的損失加上。

（4）采用torch.optim的優(yōu)化器實現(xiàn)正則化的方法，是沒問題的！只不過很容易讓人產(chǎn)生誤解，對鄙人而言，我更喜歡TensorFlow的正則化實現(xiàn)方法，只需要tf.get_collection(tf.GraphKeys.REGULARIZATION_LOSSES)，實現(xiàn)過程幾乎跟正則化的公式對應的上。

（5）Github項目源碼：點擊進入

為了，解決這些問題，我特定自定義正則化的方法，類似于TensorFlow正則化實現(xiàn)方法。

2. 如何判斷正則化作用了模型？

一般來說，正則化的主要作用是避免模型產(chǎn)生過擬合，當然啦，過擬合問題，有時候是難以判斷的。但是，要判斷正則化是否作用了模型，還是很容易的。下面我給出兩組訓練時產(chǎn)生的loss和Accuracy的log信息，一組是未加入正則化的，一組是加入正則化：

2.1 未加入正則化loss和Accuracy

優(yōu)化器采用Adam，并且設置參數(shù)weight_decay=0.0，即無正則化的方法

optimizer = optim.Adam(model.parameters(),lr=learning_rate,weight_decay=0.0)

訓練時輸出的 loss和Accuracy信息

step/epoch:0/0,Train Loss: 2.418065, Acc: [0.15625]
step/epoch:10/0,Train Loss: 5.194936, Acc: [0.34375]
step/epoch:20/0,Train Loss: 0.973226, Acc: [0.8125]
step/epoch:30/0,Train Loss: 1.215165, Acc: [0.65625]
step/epoch:40/0,Train Loss: 1.808068, Acc: [0.65625]
step/epoch:50/0,Train Loss: 1.661446, Acc: [0.625]
step/epoch:60/0,Train Loss: 1.552345, Acc: [0.6875]
step/epoch:70/0,Train Loss: 1.052912, Acc: [0.71875]
step/epoch:80/0,Train Loss: 0.910738, Acc: [0.75]
step/epoch:90/0,Train Loss: 1.142454, Acc: [0.6875]
step/epoch:100/0,Train Loss: 0.546968, Acc: [0.84375]
step/epoch:110/0,Train Loss: 0.415631, Acc: [0.9375]
step/epoch:120/0,Train Loss: 0.533164, Acc: [0.78125]
step/epoch:130/0,Train Loss: 0.956079, Acc: [0.6875]
step/epoch:140/0,Train Loss: 0.711397, Acc: [0.8125]

2.1 加入正則化loss和Accuracy

優(yōu)化器采用Adam，并且設置參數(shù)weight_decay=10.0，即正則化的權(quán)重lambda =10.0

optimizer = optim.Adam(model.parameters(),lr=learning_rate,weight_decay=10.0)

這時，訓練時輸出的 loss和Accuracy信息：

step/epoch:0/0,Train Loss: 2.467985, Acc: [0.09375]
step/epoch:10/0,Train Loss: 5.435320, Acc: [0.40625]
step/epoch:20/0,Train Loss: 1.395482, Acc: [0.625]
step/epoch:30/0,Train Loss: 1.128281, Acc: [0.6875]
step/epoch:40/0,Train Loss: 1.135289, Acc: [0.6875]
step/epoch:50/0,Train Loss: 1.455040, Acc: [0.5625]
step/epoch:60/0,Train Loss: 1.023273, Acc: [0.65625]
step/epoch:70/0,Train Loss: 0.855008, Acc: [0.65625]
step/epoch:80/0,Train Loss: 1.006449, Acc: [0.71875]
step/epoch:90/0,Train Loss: 0.939148, Acc: [0.625]
step/epoch:100/0,Train Loss: 0.851593, Acc: [0.6875]
step/epoch:110/0,Train Loss: 1.093970, Acc: [0.59375]
step/epoch:120/0,Train Loss: 1.699520, Acc: [0.625]
step/epoch:130/0,Train Loss: 0.861444, Acc: [0.75]
step/epoch:140/0,Train Loss: 0.927656, Acc: [0.625]

當weight_decay=10000.0

step/epoch:0/0,Train Loss: 2.337354, Acc: [0.15625]
step/epoch:10/0,Train Loss: 2.222203, Acc: [0.125]
step/epoch:20/0,Train Loss: 2.184257, Acc: [0.3125]
step/epoch:30/0,Train Loss: 2.116977, Acc: [0.5]
step/epoch:40/0,Train Loss: 2.168895, Acc: [0.375]
step/epoch:50/0,Train Loss: 2.221143, Acc: [0.1875]
step/epoch:60/0,Train Loss: 2.189801, Acc: [0.25]
step/epoch:70/0,Train Loss: 2.209837, Acc: [0.125]
step/epoch:80/0,Train Loss: 2.202038, Acc: [0.34375]
step/epoch:90/0,Train Loss: 2.192546, Acc: [0.25]
step/epoch:100/0,Train Loss: 2.215488, Acc: [0.25]
step/epoch:110/0,Train Loss: 2.169323, Acc: [0.15625]
step/epoch:120/0,Train Loss: 2.166457, Acc: [0.3125]
step/epoch:130/0,Train Loss: 2.144773, Acc: [0.40625]
step/epoch:140/0,Train Loss: 2.173397, Acc: [0.28125]

2.3 正則化說明

就整體而言，對比加入正則化和未加入正則化的模型，訓練輸出的loss和Accuracy信息，我們可以發(fā)現(xiàn)，加入正則化后，loss下降的速度會變慢，準確率Accuracy的上升速度會變慢，并且未加入正則化模型的loss和Accuracy的浮動比較大（或者方差比較大），而加入正則化的模型訓練loss和Accuracy，表現(xiàn)的比較平滑。

并且隨著正則化的權(quán)重lambda越大，表現(xiàn)的更加平滑。這其實就是正則化的對模型的懲罰作用，通過正則化可以使得模型表現(xiàn)的更加平滑，即通過正則化可以有效解決模型過擬合的問題。

3.自定義正則化的方法

為了解決torch.optim優(yōu)化器只能實現(xiàn)L2正則化以及懲罰網(wǎng)絡中的所有參數(shù)的缺陷，這里實現(xiàn)類似于TensorFlow正則化的方法。

3.1 自定義正則化Regularization類

這里封裝成一個實現(xiàn)正則化的Regularization類，各個方法都給出了注釋，自己慢慢看吧，有問題再留言吧

# 檢查GPU是否可用
device = torch.device("cuda" if torch.cuda.is_available() else "cpu")
# device='cuda'
print("-----device:{}".format(device))
print("-----Pytorch version:{}".format(torch.__version__))
 
class Regularization(torch.nn.Module):
 def __init__(self,model,weight_decay,p=2):
  '''
  :param model 模型
  :param weight_decay:正則化參數(shù)
  :param p: 范數(shù)計算中的冪指數(shù)值，默認求2范數(shù),
     當p=0為L2正則化,p=1為L1正則化
  '''
  super(Regularization, self).__init__()
  if weight_decay <= 0:
   print("param weight_decay can not <=0")
   exit(0)
  self.model=model
  self.weight_decay=weight_decay
  self.p=p
  self.weight_list=self.get_weight(model)
  self.weight_info(self.weight_list)
 
 def to(self,device):
  '''
  指定運行模式
  :param device: cude or cpu
  :return:
  '''
  self.device=device
  super().to(device)
  return self
 
 def forward(self, model):
  self.weight_list=self.get_weight(model)#獲得最新的權(quán)重
  reg_loss = self.regularization_loss(self.weight_list, self.weight_decay, p=self.p)
  return reg_loss
 
 def get_weight(self,model):
  '''
  獲得模型的權(quán)重列表
  :param model:
  :return:
  '''
  weight_list = []
  for name, param in model.named_parameters():
   if 'weight' in name:
    weight = (name, param)
    weight_list.append(weight)
  return weight_list
 
 def regularization_loss(self,weight_list, weight_decay, p=2):
  '''
  計算張量范數(shù)
  :param weight_list:
  :param p: 范數(shù)計算中的冪指數(shù)值，默認求2范數(shù)
  :param weight_decay:
  :return:
  '''
  # weight_decay=Variable(torch.FloatTensor([weight_decay]).to(self.device),requires_grad=True)
  # reg_loss=Variable(torch.FloatTensor([0.]).to(self.device),requires_grad=True)
  # weight_decay=torch.FloatTensor([weight_decay]).to(self.device)
  # reg_loss=torch.FloatTensor([0.]).to(self.device)
  reg_loss=0
  for name, w in weight_list:
   l2_reg = torch.norm(w, p=p)
   reg_loss = reg_loss + l2_reg
 
  reg_loss=weight_decay*reg_loss
  return reg_loss
 
 def weight_info(self,weight_list):
  '''
  打印權(quán)重列表信息
  :param weight_list:
  :return:
  '''
  print("---------------regularization weight---------------")
  for name ,w in weight_list:
   print(name)
  print("---------------------------------------------------")

3.2 Regularization使用方法

使用方法很簡單，就當一個普通Pytorch模塊來使用：例如

# 檢查GPU是否可用
device = torch.device("cuda" if torch.cuda.is_available() else "cpu")
 
print("-----device:{}".format(device))
print("-----Pytorch version:{}".format(torch.__version__))
 
weight_decay=100.0 # 正則化參數(shù)
 
model = my_net().to(device)
# 初始化正則化
if weight_decay>0:
 reg_loss=Regularization(model, weight_decay, p=2).to(device)
else:
 print("no regularization")
 
criterion= nn.CrossEntropyLoss().to(device) # CrossEntropyLoss=softmax+cross entropy
optimizer = optim.Adam(model.parameters(),lr=learning_rate)#不需要指定參數(shù)weight_decay
 
# train
batch_train_data=...
batch_train_label=...
 
out = model(batch_train_data)
 
# loss and regularization
loss = criterion(input=out, target=batch_train_label)
if weight_decay > 0:
 loss = loss + reg_loss(model)
total_loss = loss.item()
 
# backprop
optimizer.zero_grad()#清除當前所有的累積梯度
total_loss.backward()
optimizer.step()

訓練時輸出的 loss和Accuracy信息：

（1）當weight_decay=0.0時，未使用正則化

step/epoch:0/0,Train Loss: 2.379627, Acc: [0.09375]
step/epoch:10/0,Train Loss: 1.473092, Acc: [0.6875]
step/epoch:20/0,Train Loss: 0.931847, Acc: [0.8125]
step/epoch:30/0,Train Loss: 0.625494, Acc: [0.875]
step/epoch:40/0,Train Loss: 2.241885, Acc: [0.53125]
step/epoch:50/0,Train Loss: 1.132131, Acc: [0.6875]
step/epoch:60/0,Train Loss: 0.493038, Acc: [0.8125]
step/epoch:70/0,Train Loss: 0.819410, Acc: [0.78125]
step/epoch:80/0,Train Loss: 0.996497, Acc: [0.71875]
step/epoch:90/0,Train Loss: 0.474205, Acc: [0.8125]
step/epoch:100/0,Train Loss: 0.744587, Acc: [0.8125]
step/epoch:110/0,Train Loss: 0.502217, Acc: [0.78125]
step/epoch:120/0,Train Loss: 0.531865, Acc: [0.8125]
step/epoch:130/0,Train Loss: 1.016807, Acc: [0.875]
step/epoch:140/0,Train Loss: 0.411701, Acc: [0.84375]

（2）當weight_decay=10.0時，使用正則化

---------------------------------------------------
step/epoch:0/0,Train Loss: 1563.402832, Acc: [0.09375]
step/epoch:10/0,Train Loss: 1530.002686, Acc: [0.53125]
step/epoch:20/0,Train Loss: 1495.115234, Acc: [0.71875]
step/epoch:30/0,Train Loss: 1461.114136, Acc: [0.78125]
step/epoch:40/0,Train Loss: 1427.868164, Acc: [0.6875]
step/epoch:50/0,Train Loss: 1395.430054, Acc: [0.6875]
step/epoch:60/0,Train Loss: 1363.358154, Acc: [0.5625]
step/epoch:70/0,Train Loss: 1331.439697, Acc: [0.75]
step/epoch:80/0,Train Loss: 1301.334106, Acc: [0.625]
step/epoch:90/0,Train Loss: 1271.505005, Acc: [0.6875]
step/epoch:100/0,Train Loss: 1242.488647, Acc: [0.75]
step/epoch:110/0,Train Loss: 1214.184204, Acc: [0.59375]
step/epoch:120/0,Train Loss: 1186.174561, Acc: [0.71875]
step/epoch:130/0,Train Loss: 1159.148438, Acc: [0.78125]
step/epoch:140/0,Train Loss: 1133.020020, Acc: [0.65625]

（3）當weight_decay=10000.0時，使用正則化

step/epoch:0/0,Train Loss: 1570211.500000, Acc: [0.09375]
step/epoch:10/0,Train Loss: 1522952.125000, Acc: [0.3125]
step/epoch:20/0,Train Loss: 1486256.125000, Acc: [0.125]
step/epoch:30/0,Train Loss: 1451671.500000, Acc: [0.25]
step/epoch:40/0,Train Loss: 1418959.750000, Acc: [0.15625]
step/epoch:50/0,Train Loss: 1387154.000000, Acc: [0.125]
step/epoch:60/0,Train Loss: 1355917.500000, Acc: [0.125]
step/epoch:70/0,Train Loss: 1325379.500000, Acc: [0.125]
step/epoch:80/0,Train Loss: 1295454.125000, Acc: [0.3125]
step/epoch:90/0,Train Loss: 1266115.375000, Acc: [0.15625]
step/epoch:100/0,Train Loss: 1237341.000000, Acc: [0.0625]
step/epoch:110/0,Train Loss: 1209186.500000, Acc: [0.125]
step/epoch:120/0,Train Loss: 1181584.250000, Acc: [0.125]
step/epoch:130/0,Train Loss: 1154600.125000, Acc: [0.1875]
step/epoch:140/0,Train Loss: 1128239.875000, Acc: [0.125]

對比torch.optim優(yōu)化器的實現(xiàn)L2正則化方法，這種Regularization類的方法也同樣達到正則化的效果，并且與TensorFlow類似，loss把正則化的損失也計算了。

此外更改參數(shù)p，如當p=0表示L2正則化，p=1表示L1正則化。