pytorch 实现L2和L1正则化regularization的操作

1.torch.optim优化器实现L2正则化

torch.optim集成了很多优化器，如SGD，Adadelta，Adam，Adagrad，RMSprop等，这些优化器自带的一个参数weight_decay，用于指定权值衰减率，相当于L2正则化中的λ参数，注意torch.optim集成的优化器只有L2正则化方法，你可以查看注释，参数weight_decay 的解析是：

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

使用torch.optim的优化器，可如下设置L2正则化

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

但是这种方法存在几个问题，

（1）一般正则化，只是对模型的权重W参数进行惩罚，而偏置参数b是不进行惩罚的，而torch.optim的优化器weight_decay参数指定的权值衰减是对网络中的所有参数，包括权值w和偏置b同时进行惩罚。很多时候如果对b 进行L2正则化将会导致严重的欠拟合，因此这个时候一般只需要对权值w进行正则即可。（PS：这个我真不确定，源码解析是 weight decay (L2 penalty) ，但有些网友说这种方法会对参数偏置b也进行惩罚，可解惑的网友给个明确的答复）

（2）缺点：torch.optim的优化器固定实现L2正则化，不能实现L1正则化。如果需要L1正则化，可如下实现：

（3）根据正则化的公式，加入正则化后，loss会变原来大，比如weight_decay=1的loss为10，那么weight_decay=100时，loss输出应该也提高100倍左右。而采用torch.optim的优化器的方法，如果你依然采用loss_fun= nn.CrossEntropyLoss()进行计算loss，你会发现，不管你怎么改变weight_decay的大小，loss会跟之前没有加正则化的大小差不多。这是因为你的loss_fun损失函数没有把权重W的损失加上。

（4）采用torch.optim的优化器实现正则化的方法，是没问题的！只不过很容易让人产生误解，对鄙人而言，我更喜欢TensorFlow的正则化实现方法，只需要tf.get_collection(tf.GraphKeys.REGULARIZATION_LOSSES)，实现过程几乎跟正则化的公式对应的上。

（5）Github项目源码：点击进入

为了，解决这些问题，我特定自定义正则化的方法，类似于TensorFlow正则化实现方法。

2. 如何判断正则化作用了模型？

一般来说，正则化的主要作用是避免模型产生过拟合，当然啦，过拟合问题，有时候是难以判断的。但是，要判断正则化是否作用了模型，还是很容易的。下面我给出两组训练时产生的loss和Accuracy的log信息，一组是未加入正则化的，一组是加入正则化：

2.1 未加入正则化loss和Accuracy

优化器采用Adam，并且设置参数weight_decay=0.0，即无正则化的方法

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

训练时输出的 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 加入正则化loss和Accuracy

优化器采用Adam，并且设置参数weight_decay=10.0，即正则化的权重lambda =10.0

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

这时，训练时输出的 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]

当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 正则化说明

就整体而言，对比加入正则化和未加入正则化的模型，训练输出的loss和Accuracy信息，我们可以发现，加入正则化后，loss下降的速度会变慢，准确率Accuracy的上升速度会变慢，并且未加入正则化模型的loss和Accuracy的浮动比较大（或者方差比较大），而加入正则化的模型训练loss和Accuracy，表现的比较平滑。

并且随着正则化的权重lambda越大，表现的更加平滑。这其实就是正则化的对模型的惩罚作用，通过正则化可以使得模型表现的更加平滑，即通过正则化可以有效解决模型过拟合的问题。

3.自定义正则化的方法

为了解决torch.optim优化器只能实现L2正则化以及惩罚网络中的所有参数的缺陷，这里实现类似于TensorFlow正则化的方法。

3.1 自定义正则化Regularization类

这里封装成一个实现正则化的Regularization类，各个方法都给出了注释，自己慢慢看吧，有问题再留言吧

# 检查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:正则化参数
  :param p: 范数计算中的幂指数值，默认求2范数,
     当p=0为L2正则化,p=1为L1正则化
  '''
  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):
  '''
  指定运行模式
  :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)#获得最新的权重
  reg_loss = self.regularization_loss(self.weight_list, self.weight_decay, p=self.p)
  return reg_loss

 def get_weight(self,model):
  '''
  获得模型的权重列表
  :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):
  '''
  计算张量范数
  :param weight_list:
  :param p: 范数计算中的幂指数值，默认求2范数
  :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):
  '''
  打印权重列表信息
  :param weight_list:
  :return:
  '''
  print("---------------regularization weight---------------")
  for name ,w in weight_list:
   print(name)
  print("---------------------------------------------------")

3.2 Regularization使用方法

使用方法很简单，就当一个普通Pytorch模块来使用：例如

# 检查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 # 正则化参数

model = my_net().to(device)
# 初始化正则化
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)#不需要指定参数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()#清除当前所有的累积梯度
total_loss.backward()
optimizer.step()

训练时输出的 loss和Accuracy信息：

（1）当weight_decay=0.0时，未使用正则化

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）当weight_decay=10.0时，使用正则化

---------------------------------------------------
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）当weight_decay=10000.0时，使用正则化

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]

对比torch.optim优化器的实现L2正则化方法，这种Regularization类的方法也同样达到正则化的效果，并且与TensorFlow类似，loss把正则化的损失也计算了。

此外更改参数p，如当p=0表示L2正则化，p=1表示L1正则化。

4. Github项目源码下载

《Github项目源码》点击进入

以上为个人经验，希望能给大家一个参考，也希望大家多多支持我们。如有错误或未考虑完全的地方，望不吝赐教。