Repository: pytorch
Issue: [proposed feature] Eve: Improving Stochastic Gradient Descent with Feedback
Labels: feature,module: optimizer,triaged

Hi all,

I implemented a paper "Improving Stochastic Gradient Descent with Feedback" as called [Eve](https://arxiv.org/abs/1611.01505).
Eve is a modified version of Adam, and outperforms other SGD algorithms on some benchmark tasks including image classification.
Please, give me any advice and code review.

The code is uploaded in this [gist](https://gist.github.com/snowyday/19b959b268d3af7785b2dd0e2f37f6bb), and below:
```python
import math
# from .optimizer import Optimizer
from torch.optim import Optimizer


class Eve(Optimizer):
    """Implements Eve (Adam with feedback) algorithm.
    
    It has been proposed in `Improving Stochastic Gradient Descent with Feedback, `_.
    
    Arguments:
        params (iterable): iterable of parameters to optimize or dicts defining
            parameter groups
        lr (float, optional): learning rate (default: 1e-2)
        betas (Tuple[float, float, float], optional): coefficients used for computing
            running averages of gradient and its square (default: (0.9, 0.999, 0.999))
        thr ((Tuple[float, float], optional): lower and upper threshold for relative change 
            (default: (0.1, 10))
        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)
        
    .. _Eve\: Improving Stochastic Gradient Descent with Feedback
        https://arxiv.org/abs/1611.01505
    """

    def __init__(self, params, lr=1e-2, betas=(0.9, 0.999, 0.999), eps=1e-8, thr=(0.1, 10), weight_decay=0):
        defaults = dict(lr=lr, betas=betas, eps=eps, thr=thr, weight_decay=weight_decay)
        super(Eve, self).__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.
        """

        if closure is not None:
            loss = closure()
            loss_val = loss.data[0]
        else:
            raise ValueError("Eve requires a value of the loss function.")

        for group in self.param_groups:
            for p in group['params']:

                grad = p.grad.data
                state = self.state[id(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_()
                    # Previous loss value
                    state['loss_hat_prev'] = loss_val
                    # Feed-back from the loss function
                    state['decay_rate'] = 1

                exp_avg, exp_avg_sq = state['exp_avg'], state['exp_avg_sq']
                beta1, beta2, beta3 = group['betas']
                thl, thu = group['thr']
                loss_hat_prev = state['loss_hat_prev']

                state['step'] += 1

                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)

                bias_correction1 = 1 - beta1 ** state['step']
                bias_correction2 = 1 - beta2 ** state['step']
                step_size = group['lr'] * math.sqrt(bias_correction2) / bias_correction1

                if state['step'] > 1:
                    if loss_val >= loss_hat_prev:
                        lower_bound = thl + 1
                        upper_bound = thu + 1
                    else:
                        lower_bound = 1 / (thu + 1)
                        upper_bound = 1 / (thl + 1)

                    clip = min(max(lower_bound, loss_val / loss_hat_prev), upper_bound)
                    loss_hat = clip * loss_hat_prev
                    relative_change = abs(loss_hat - loss_hat_prev) / min(loss_hat, loss_hat_prev)
                    state['decay_rate'] = beta3 * state['decay_rate'] + (1 - beta3) * relative_change
                    state['loss_hat_prev'] = loss_hat

                denom = exp_avg_sq.sqrt().mul_(state['decay_rate']).add_(group['eps'])

                p.data.addcdiv_(-step_size, exp_avg, denom)

        return loss
```