Performs a single optimization step.

        Arguments:
            closure (callable, optional): A closure that reevaluates the model
                and returns the loss.

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')

                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)
                    # Exponential moving average of squared gradient values
                    state['exp_avg_sq'] = torch.zeros_like(p.data)

                exp_avg, exp_avg_sq = state['exp_avg'], state['exp_avg_sq']
                beta1, beta2 = group['b1'], group['b2']

                state['step'] += 1

                # Add grad clipping
                if group['max_grad_norm'] > 0:
                    clip_grad_norm_(p, group['max_grad_norm'])

                # 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['e'])

                bias_correction1 = 1 - beta1 ** state['step']
                bias_correction2 = 1 - beta2 ** state['step']

                lr_scheduled = group['lr']
                lr_scheduled *= group['schedule'].get_lr(state['step'])

                step_size = lr_scheduled * math.sqrt(bias_correction2) / bias_correction1

                p.data.addcdiv_(-step_size, exp_avg, denom)

                # Add weight decay at the end (fixed version)
                if (len(p.size()) > 1 or group['vector_l2']) and group['weight_decay'] > 0:
                    p.data.add_(-lr_scheduled * group['weight_decay'], p.data)

        return loss