1. 調用方法
torch.optim.Adam(params, lr=0.001, betas=(0.9, 0.999), eps=1e-08, weight_decay=0, amsgrad=False)
參數:
weight_decay : 這裏是採用權重衰減,權重衰減的係數
amsgrad:在更新時,是否保留梯度的二階歷史信息
2.源碼
源碼中的實現,參照最後一幅圖中L2正則化的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] # 之前的step累計數據
# 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'] # 上次的r與s
if amsgrad:
# asmgrad優化方法是針對Adam的改進,通過添加額外的約束,使學習率始終爲正值。
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']
# 序號對應最後一幅圖中序號
if group['weight_decay'] != 0: # 進行權重衰減(實際是L2正則化)
# 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.計算m(t): m(t)=beta_1*m(t-1)+(1-beta_1)*grad
exp_avg.mul_(beta1).add_(1 - beta1, grad)
# 8.計算v(t): v(t)= beta_2*v(t-1)+(1-beta_2)*grad^2
exp_avg_sq.mul_(beta2).addcmul_(1 - beta2, grad, grad)
if amsgrad:
# Maintains the maximum of all 2nd moment running avg. till now
# 迭代改變max_exp_avg_sq的值(取最大值),傳到下一次,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:
# 計算sqrt(v(t))+epsilon
# 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
對最後一步更新
上式取,即可與最後一幅圖中序號12等價
算法:
(《深度學習》書中,pytorch中Adam不採用下面方式)
3. adam中權重衰減與L2正則化的關係
在sgd中,權重衰減和L2正則化等價,在adam等自適應優化算法(AdaGrad/RMSProp等)中,不等價。
在pytorch中的adam中,實際使用的是L2正則化(下圖中使用紅色部分),adamw算法中使用weight_decay(下圖中暗黃色部分),兩者的區別在於使用位置不同,其他部分都相同。