2023年11月29日发(作者：)
pytorch中Adam优化器源码解读
1. 调⽤⽅法
torch.optim.Adam(params, lr=0.001, betas=(0.9, 0.999), eps=1e-08, weight_decay=0, amsgrad=False)
参数：
weight_decay : 这⾥是采⽤权重衰减，权重衰减的系数
amsgrad：在更新时，是否保留梯度的⼆阶历史信息
2.源码
源码中的实现，参照最后⼀幅图中L2正则化的Adam。
def step(self, closure=None):
"""Performs a single optimization step.
Arguments:
closure (callable, optional): A closure that reevaluates the model
and returns the loss.
"""
loss = None
if closure is not None:
loss = closure()
for group in self.param_groups:
for p in group['params']:
if p.grad is None:
continue
grad = p.grad.data
if grad.is_sparse:
raise RuntimeError('Adam does not support sparse gradients, please consider SparseAdam instead')
amsgrad = group['amsgrad']
state = self.state[p] # step
之前的累计数据
# State initialization
if len(state) == 0:
state['step'] = 0
# Exponential moving average of gradient values
state['exp_avg'] = torch.zeros_like(p.data) # [batch, seq]
# Exponential moving average of squared gradient values
state['exp_avg_sq'] = torch.zeros_like(p.data)
if amsgrad:
# Maintains max of all exp. moving avg. of sq. grad. values
state['max_exp_avg_sq'] = torch.zeros_like(p.data)
exp_avg, exp_avg_sq = state['exp_avg'], state['exp_avg_sq'] # rs
上次的与
if amsgrad:
# asmgradAdam
优化⽅法是针对的改进，通过添加额外的约束，使学习率始终为正值。
max_exp_avg_sq = state['max_exp_avg_sq']
beta1, beta2 = group['betas']
state['step'] += 1
bias_correction1 = 1 - beta1 ** state['step']
bias_correction2 = 1 - beta2 ** state['step']
#
序号对应最后⼀幅图中序号
if group['weight_decay'] != 0: # (L2
进⾏权重衰减实际是正则化）
# 6. grad(t)=grad(t-1)+ weight*p(t-1)
grad.add_(group['weight_decay'], p.data)
# Decay the first and second moment running average coefficient
# 7.m(t): m(t)=beta_1*m(t-1)+(1-beta_1)*grad
计算
exp_avg.mul_(beta1).add_(1 - beta1, grad)
# 8.v(t): v(t)= beta_2*v(t-1)+(1-beta_2)*grad^2
计算
# 8.v(t): v(t)= beta_2*v(t-1)+(1-beta_2)*grad^2
计算
exp_avg_sq.mul_(beta2).addcmul_(1 - beta2, grad, grad)
if amsgrad:
# Maintains the maximum of all 2nd moment running avg. till now
# max_exp_avg_sq
迭代改变的值（取最⼤值），传到下⼀次，保留之前的梯度信息。
torch.max(max_exp_avg_sq, exp_avg_sq, out=max_exp_avg_sq)
# Use the max. for normalizing running avg. of gradient
denom = (max_exp_avg_sq.sqrt() / math.sqrt(bias_correction2)).add_(group['eps'])
else:
# sqrt(v(t))+epsilon
计算
# sqrt(v(t))+eps = denom = sqrt(v(t))/sqrt(1-beta_2^t)+eps
denom = (exp_avg_sq.sqrt() / math.sqrt(bias_correction2)).add_(group['eps'])
# step_size=lr/bias_correction1=lr/(1-beta_1^t)
step_size = group['lr'] / bias_correction1
#p(t)=p(t-1)-step_size*m(t)/denom
p.data.addcdiv_(-step_size, exp_avg, denom)
return loss
对最后⼀步更新
1−β
2
t
v
tϵ
denom==
1−β
t
2
+ϵ
1+
t
1−β
2
v^
t
ϵ
=
1+
1−β
2
t
p(t)=p(t−1)−step_size∗m(t)/denom
lr
1
t
=p(t−1)−∗
1−β
2
m(t)∗
denom
ϵ
^m
t
lr∗
t
1−β
2
v^
t
=p(t−1)−∗(1+)
上式取，即可与最后⼀幅图中序号12等价
α=(1+)
算法：
ϵ
t
1−β
2
（《深度学习》书中，pytorch中Adam不采⽤下⾯⽅式）
3. adam中权重衰减与L2正则化的关系
在sgd中，权重衰减和L2正则化等价，在adam等⾃适应优化算法（AdaGrad/RMSProp等）中，不等价。
在pytorch中的adam中，实际使⽤的是L2正则化(下图中使⽤红⾊部分），adamw算法中使⽤weight_decay（下图中暗黄⾊部分），两者
的区别在于使⽤位置不同，其他部分都相同。
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