在Pytorch中实现WNGrad？

Question

我正在尝试在pytorch中实现WNGrad（技术上WN-Adam，论文中的算法4）optimizier（WNGrad）。我之前从未在pytorch中实现过优化器，因此我不知道我是否已正确完成（我从adam实现开始）。优化器没有取得太大进展并且像我预期的那样下降（bj值只能单调增加，这很快发生，所以没有进展）但我猜我有一个bug。标准优化器（Adam，SGD）在我试图优化的同一模型上工作正常。

这种实现看起来是否正确？

from torch.optim import Optimizer

class WNAdam(Optimizer):
    """Implements WNAdam algorithm.

    It has been proposed in `WNGrad: Learn the Learning Rate in Gradient Descent`_.

    Arguments:
        params (iterable): iterable of parameters to optimize or dicts defining
            parameter groups
        lr (float, optional): learning rate (default: 0.1)
        beta1 (float, optional): exponential smoothing coefficient for gradient.
                                When beta=0 this implements WNGrad.

    .. _WNGrad\: Learn the Learning Rate in Gradient Descent:
        https://arxiv.org/abs/1803.02865
    """

    def __init__(self, params, lr=0.1, beta1=0.9):
        if not 0.0 <= beta1 < 1.0:
            raise ValueError("Invalid beta1 parameter: {}".format(beta1))
        defaults = dict(lr=lr, beta1=beta1)
        super().__init__(params, defaults)

    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
                state = self.state[p]

                # State initialization
                if len(state) == 0:
                    state['step'] = 0
                    # Exponential moving average of gradient values
                    state['exp_avg'] = torch.zeros_like(p.data)
                    # Learning rate adjustment
                    state['bj'] = 1.0

                exp_avg = state['exp_avg']
                beta1 = group['beta1']

                state['step'] += 1
                state['bj'] += (group['lr']**2)/(state['bj'])*grad.pow(2).sum()

                # update exponential moving average
                exp_avg.mul_(beta1).add_(1 - beta1, grad)

                bias_correction = 1 - beta1 ** state['step']
                p.data.sub_(group['lr'] / state['bj'] / bias_correction, exp_avg)
        return loss

Answer 1

WNGrad论文表明它受批量（和重量）标准化的启发。你应该使用关于权重维度的L2范数（不要总结）作为show in this algorithm