1.torch.optim優化器實現L2正則化
torch.optim集成了很多優化器，如SGD，Adadelta，Adam，Adagrad，RMSprop等，這些優化器自帶的一個參數weight_decay，用于指定權值衰減率，相當于L2正則化中的λ參數，注意torch.optim集成的優化器只有L2正則化方法，你可以查看注釋，參數weight_decay 的解析是：
weight_decay (float, optional): weight decay (L2 penalty) (default: 0)
使用torch.optim的優化器，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，只是對模型的權重W參數進行懲罰，而偏置參數b是不進行懲罰的，而torch.optim的優化器weight_decay參數指定的權值衰減是對網絡中的所有參數，包括權值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) ，但有些網友說這種方法會對參數偏置b也進行懲罰，可解惑的網友給個明確的答復）
（2）缺點：torch.optim的優化器固定實現L2正則化，不能實現L1正則化。如果需要L1正則化，可如下實現：
（3）根據正則化的公式，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的優化器的方法，如果你依然采用loss_fun= nn.CrossEntropyLoss()進行計算loss，你會發現，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損失函數沒有把權重W的損失加上。
（4）采用torch.optim的優化器實現正則化的方法，是沒問題的！只不過很容易讓人產生誤解，對鄙人而言，我更喜歡TensorFlow的正則化實現方法，只需要tf.get_collection(tf.GraphKeys.REGULARIZATION_LOSSES)，實現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
優化器采用Adam，并且設置參數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
優化器采用Adam，并且設置參數weight_decay=10.0，即正則化的權重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，我們可以發現，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，表現的比較平滑。
并且隨著正則化的權重lambda越大，表現的更加平滑。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優化器只能實現L2正則化以及懲罰網絡中的所有參數的缺陷，這里實現類似于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
:param p: 范數計算中的冪指數值，默認求2范數,
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
:param weight_list:
:param p: 范數計算中的冪指數值，默認求2范數
: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
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優化器的實現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p，如當p=0表示L2正則化，p=1表示L1正則化。
4. Github項目源碼下載
《Github項目源碼》點擊進入
以上為個人經驗，希望能給大家一個參考，也希望大家多多支持腳本之家。如有錯誤或未考慮完全的地方，望不吝賜教。
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