pytorch中SGD代碼解讀

調用方法：

torch.optim.SGD(params, lr=<required parameter>, momentum=0, dampening=0, weight_decay=0, nesterov=False)

momentum: 動量參數
dampen ing：梯度抑制參數
weight_cay:L2的參數
nesterov：是否使用neterov動量

    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:
            weight_decay = group['weight_decay'] # 權重衰減係數
            momentum = group['momentum'] # 動量因子，0.9或0.8
            dampening = group['dampening'] # 梯度抑制因子
            nesterov = group['nesterov'] # 是否使用nesterov動量

            for p in group['params']:
                if p.grad is None:
                    continue
                d_p = p.grad.data
                if weight_decay != 0: # 進行正則化
                	# add_表示原處改變，d_p = d_p + weight_decay*p.data
                    d_p.add_(weight_decay, p.data)
                if momentum != 0:
                    param_state = self.state[p] # 之前的累計的數據，v(t-1)
                    # 進行動量累計計算
                    if 'momentum_buffer' not in param_state:
                        buf = param_state['momentum_buffer'] = torch.clone(d_p).detach()
                    else:
                    	# 之前的動量
                        buf = param_state['momentum_buffer']
                        # buf= buf*momentum + （1-dampening）*d_p
                        buf.mul_(momentum).add_(1 - dampening, d_p)
                    if nesterov: # 使用neterov動量
                    	# d_p= d_p + momentum*buf
                        d_p = d_p.add(momentum, buf)
                    else:
                        d_p = buf
				# p = p - lr*d_p
                p.data.add_(-group['lr'], d_p)

        return loss

Pytorch中的SGD採用下述方式

也即

代碼中，
d_p = d_p + weight_decayp.data # 權重衰減，這裏實際上是做的 L2正則
buf = bufmomentum + （1-dampening）d_p # 計算動量，即v
若採用nesterov動量
d_p= d_p + momentumbuf
否則 d_p = buf
最後更新
p = p - lr*d_p

說明一下，L2正則的地方
$loss=||y-y^{*}||+\frac{\lambda}{2}||w||^2$
求完導數後
$\frac{\partial loss}{\partial w}=\frac{\partial ||y-y^{*}||}{\partial w}+\lambda*w$
上式右邊的前半部分在loss.backward()已經求出，後半部分既是代碼中進行正則化的部分，計算完畢再進行參數更新。weight_decay即是$\lambda$.
普通不帶動量的SGD中權重衰減和L2正則是等價的。

在這裏，還需要注意，採用d_p = p.grad.data修改時，會直接修改p.grad.data的數據