Adam with Hypergradient Descent

import torch
import math
import torch.optim
from torch.optim.optimizer import Optimizer, required
class AdamHD(Optimizer):
    """Implements Adam algorithm.
    It has been proposed in `Adam: A Method for Stochastic Optimization`_.
    Arguments:
        params (iterable): iterable of parameters to optimize or dicts defining
            parameter groups
        lr (float, optional): learning rate (default: 1e-3)
        betas (Tuple[float, float], optional): coefficients used for computing
            running averages of gradient and its square (default: (0.9, 0.999))
        eps (float, optional): term added to the denominator to improve
            numerical stability (default: 1e-8)
        weight_decay (float, optional): weight decay (L2 penalty) (default: 0)
    .. _Adam\: A Method for Stochastic Optimization:
        https://arxiv.org/abs/1412.6980
    """

    def __init__(self, params, lr=1e-3, betas=(0.9, 0.999), eps=1e-8,
                 weight_decay=0,beta=1e-8):
        defaults = dict(lr=lr, betas=betas, eps=eps,
                        weight_decay=weight_decay)
        super(AdamHD, self).__init__(params, defaults)
        self.beta = beta

    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'] = grad.new().resize_as_(grad).zero_()
                    # Exponential moving average of squared gradient values
                    state['exp_avg_sq'] = grad.new().resize_as_(grad).zero_()
                    state['u'] = grad.new().resize_as_(grad).zero_()
                    

                exp_avg, exp_avg_sq = state['exp_avg'], state['exp_avg_sq']
                beta1, beta2 = group['betas']
                


                state['step'] += 1
               
                # Update hpyergradient
                group['lr'] = group['lr'] - self.beta*torch.dot(grad,state['u'])
                # lr.add_(-self.beta*grad*(-exp_avg/self.denom
                
                if group['weight_decay'] != 0:
                    grad = grad.add(group['weight_decay'], p.data)
                
                
                # Decay the first and second moment running average coefficient
                exp_avg.mul_(beta1).add_(1 - beta1, grad)
                exp_avg_sq.mul_(beta2).addcmul_(1 - beta2, grad, grad)

                denom = exp_avg_sq.sqrt().add_(group['eps'])

                bias_correction1 = 1 - beta1 ** state['step']
                bias_correction2 = 1 - beta2 ** state['step']
                
                step_size = math.sqrt(bias_correction2) / bias_correction1
                
                state['u']= -step_size * exp_avg / denom
                
                p.data.add_(group['lr']*state['u'])

        return loss

This implementation is wrong. The dot product of the gradient and u is being taking component-wise. However, in the method of hypergradients described in Adam: A Method for Stochastic Optimization, the dot product has to be taken using the whole gradient (or its estimator using minibatches) and the whole vector u.