为Adam Optimizer加权衰减的正确方法是什么？

Question

由于Adam Optimizer保持一对平均值,如渐变的均值/方差,我想知道它应该如何正确处理重量衰减.我已经看到了两种实现它的方法.

1. 仅根据客观损失,每个小批量明确的衰减权重更新梯度的均值/方差.(以下代码摘自https://github.com/dmlc/mxnet/blob/v0.7.0/python/mxnet/optimizer.py)

   weight[:] -= lr*mean/(sqrt(variance) + self.epsilon)
   
   wd = self._get_wd(index)
   if wd > 0.:
       weight[:] -= (lr * wd) * weight
   

2. 根据客观损失+正则化损失更新梯度的均值/方差,并像往常一样更新权重.(以下代码摘自https://github.com/dmlc/mxnet/blob/master/src/operator/optimizer_op-inl.h#L210)

   grad = scalar<DType>(param.rescale_grad) * grad +
   scalar<DType>(param.wd) * weight;
   // stuff
   Assign(out, req[0],
      weight -
      scalar<DType>(param.lr) * mean /
      (F<square_root>(var) + scalar<DType>(param.epsilon)));
   

这两种方法有时在训练结果上显示出显着差异.而我实际上认为第一个更有意义(并且发现它会不时地提供更好的结果).Caffe和旧版本的mxnet遵循第一种方法,而火炬,tensorflow和新版本的mxnet遵循第二种方法.

真的很感谢你的帮助!

Answer 1

编辑:也看到这个PR刚刚合并到TF.

当使用纯SGD(没有动量),为优化器,重量衰变是一回事添加L2-正则化项的损失.使用任何其他优化器时,情况并非如此.

重量衰减(不知道如何在这里使用TeX,请原谅我的伪符号):

w[t+1] = w[t] - learning_rate * dw - weight_decay * w

L2正则:

loss = actual_loss + lambda * 1/2 sum(||w||_2 for w in network_params)

计算L2正则化中的额外项的梯度给出lambda * w并因此将其插入SGD更新方程中

dloss_dw = dactual_loss_dw + lambda * w
w[t+1] = w[t] - learning_rate * dw

与重量衰减相同,但lambda与重量相混合learning_rate.任何其他优化器,即使是具有动量的SGD,也会为L2正则化提供不同的权重衰减更新规则!有关更多详细信息,请参阅" 修复Adam中的重量衰减 "一文.(编辑:AFAIK,这一1987年的Hinton论文引入了"权重衰减",字面意思是"每次权重更新,其数量也减少0.4%",第10页)

话虽如此,TensorFlow似乎还没有支持"适当"的体重衰减.讨论它有一些问题,特别是因为上面的论文.

实现它的一种可能方法是编写一个op,在每个优化器步骤之后手动执行衰减步骤.一种不同的方式,就是我目前正在做的,就是使用额外的SGD优化器来减轻重量,并将其"附加"到你的身上train_op.不过,这些都只是粗略的解决方案.我目前的代码:

# In the network definition:
with arg_scope([layers.conv2d, layers.dense],
               weights_regularizer=layers.l2_regularizer(weight_decay)):
    # define the network.

loss = # compute the actual loss of your problem.
train_op = optimizer.minimize(loss, global_step=global_step)
if args.weight_decay not in (None, 0):
    with tf.control_dependencies([train_op]):
        sgd = tf.train.GradientDescentOptimizer(learning_rate=1.0)
        train_op = sgd.minimize(tf.add_n(tf.get_collection(tf.GraphKeys.REGULARIZATION_LOSSES)))

这有点使用了TensorFlow提供的簿记.注意,arg_scope将每个层的L2正则化项附加到REGULARIZATION_LOSSES图形密钥,然后我使用SGD对其进行求和和优化,如上所示,SGD对应于实际的权重衰减.

希望有所帮助,如果有人为此获得更好的代码片段,或者TensorFlow更好地实现它(即在优化器中),请分享.

Answer 2

我遇到了同样的问题。我认为我从这里获得的这段代码对您有用。它通过继承自 来实现权重衰减 adam 优化器tf.train.Optimizer。这是我发现的最干净的解决方案：

class AdamWeightDecayOptimizer(tf.train.Optimizer):
"""A basic Adam optimizer that includes "correct" L2 weight decay."""

def __init__(self,
             learning_rate,
             weight_decay_rate=0.0,
             beta_1=0.9,
             beta_2=0.999,
             epsilon=1e-6,
             exclude_from_weight_decay=None,
             name="AdamWeightDecayOptimizer"):
  """Constructs a AdamWeightDecayOptimizer."""
  super(AdamWeightDecayOptimizer, self).__init__(False, name)

  self.learning_rate = learning_rate
  self.weight_decay_rate = weight_decay_rate
  self.beta_1 = beta_1
  self.beta_2 = beta_2
  self.epsilon = epsilon
  self.exclude_from_weight_decay = exclude_from_weight_decay

def apply_gradients(self, grads_and_vars, global_step=None, name=None):
  """See base class."""
  assignments = []
  for (grad, param) in grads_and_vars:
    if grad is None or param is None:
      continue

    param_name = self._get_variable_name(param.name)

    m = tf.get_variable(
        name=param_name + "/adam_m",
        shape=param.shape.as_list(),
        dtype=tf.float32,
        trainable=False,
        initializer=tf.zeros_initializer())
    v = tf.get_variable(
        name=param_name + "/adam_v",
        shape=param.shape.as_list(),
        dtype=tf.float32,
        trainable=False,
        initializer=tf.zeros_initializer())

    # Standard Adam update.
    next_m = (
        tf.multiply(self.beta_1, m) + tf.multiply(1.0 - self.beta_1, grad))
    next_v = (
        tf.multiply(self.beta_2, v) + tf.multiply(1.0 - self.beta_2,
                                                  tf.square(grad)))

    update = next_m / (tf.sqrt(next_v) + self.epsilon)

    # Just adding the square of the weights to the loss function is *not*
    # the correct way of using L2 regularization/weight decay with Adam,
    # since that will interact with the m and v parameters in strange ways.
    #
    # Instead we want ot decay the weights in a manner that doesn't interact
    # with the m/v parameters. This is equivalent to adding the square
    # of the weights to the loss with plain (non-momentum) SGD.
    if self._do_use_weight_decay(param_name):
      update += self.weight_decay_rate * param

    update_with_lr = self.learning_rate * update

    next_param = param - update_with_lr

    assignments.extend(
        [param.assign(next_param),
         m.assign(next_m),
         v.assign(next_v)])
  return tf.group(*assignments, name=name)

def _do_use_weight_decay(self, param_name):
  """Whether to use L2 weight decay for `param_name`."""
  if not self.weight_decay_rate:
    return False
  if self.exclude_from_weight_decay:
    for r in self.exclude_from_weight_decay:
      if re.search(r, param_name) is not None:
        return False
  return True

def _get_variable_name(self, param_name):
  """Get the variable name from the tensor name."""
  m = re.match("^(.*):\\d+$", param_name)
  if m is not None:
    param_name = m.group(1)
  return param_name

您可以通过以下方式使用它（我做了一些更改以使其在更一般的上下文中有用），该函数将返回一个train_op可以在会话中使用的：

def create_optimizer(loss, init_lr, num_train_steps, num_warmup_steps):
  """Creates an optimizer training op."""
  global_step = tf.train.get_or_create_global_step()

  learning_rate = tf.constant(value=init_lr, shape=[], dtype=tf.float32)

  # Implements linear decay of the learning rate.
  learning_rate = tf.train.polynomial_decay(
      learning_rate,
      global_step,
      num_train_steps,
      end_learning_rate=0.0,
      power=1.0,
      cycle=False)

  # Implements linear warmup. I.e., if global_step < num_warmup_steps, the
  # learning rate will be `global_step/num_warmup_steps * init_lr`.
  if num_warmup_steps:
    global_steps_int = tf.cast(global_step, tf.int32)
    warmup_steps_int = tf.constant(num_warmup_steps, dtype=tf.int32)

    global_steps_float = tf.cast(global_steps_int, tf.float32)
    warmup_steps_float = tf.cast(warmup_steps_int, tf.float32)

    warmup_percent_done = global_steps_float / warmup_steps_float
    warmup_learning_rate = init_lr * warmup_percent_done

    is_warmup = tf.cast(global_steps_int < warmup_steps_int, tf.float32)
    learning_rate = (
        (1.0 - is_warmup) * learning_rate + is_warmup * warmup_learning_rate)

  # It is recommended that you use this optimizer for fine tuning, since this
  # is how the model was trained (note that the Adam m/v variables are NOT
  # loaded from init_checkpoint.)
  optimizer = AdamWeightDecayOptimizer(
      learning_rate=learning_rate,
      weight_decay_rate=0.01,
      beta_1=0.9,
      beta_2=0.999,
      epsilon=1e-6)


  tvars = tf.trainable_variables()
  grads = tf.gradients(loss, tvars)

  # You can do clip gradients if you need in this step(in general it is not neccessary)
  # (grads, _) = tf.clip_by_global_norm(grads, clip_norm=1.0)

  train_op = optimizer.apply_gradients(
      zip(grads, tvars), global_step=global_step)

  # Normally the global step update is done inside of `apply_gradients`.
  # However, `AdamWeightDecayOptimizer` doesn't do this. But if you use
  # a different optimizer, you should probably take this line out.
  new_global_step = global_step + 1
  train_op = tf.group(train_op, [global_step.assign(new_global_step)])
  return train_op