"""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 = LAMBOptimizer(

learning_rate=learning_rate,

weight_decay_rate=0.01,

beta_1=0.9,

beta_2=0.999,

epsilon=1e-6,

exclude_from_weight_decay=["LayerNorm", "layer_norm", "bias"])

if use_tpu:

optimizer = tf.contrib.tpu.CrossShardOptimizer(optimizer)

tvars = tf.trainable_variables()

grads = tf.gradients(loss, tvars)

# This is how the model was pre-trained.

(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)])

"""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)

"""

LAMBOptimizer optimizer.

https://github.com/ymcui/LAMB_Optimizer_TF

# IMPORTANT NOTE

- This is NOT an official implementation.

- LAMB optimizer is changed from arXiv v1 ~ v3.

- We implement v3 version (which is the latest version on June, 2019.).

- Our implementation is based on `AdamWeightDecayOptimizer` in BERT (provided by Google).

# References

- Large Batch Optimization for Deep Learning: Training BERT in 76 minutes. https://arxiv.org/abs/1904.00962v3

- BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding. https://arxiv.org/abs/1810.04805

# Parameters

- There is nothing special, just the same as `AdamWeightDecayOptimizer`.

"""

def __init__(self,

learning_rate,

weight_decay_rate=0.01,

beta_1=0.9,

beta_2=0.999,

epsilon=1e-6,

exclude_from_weight_decay=None,

name="LAMBOptimizer"):

"""Constructs a LAMBOptimizer."""

super(LAMBOptimizer, 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 + "/lamb_m",

shape=param.shape.as_list(),

dtype=tf.float32,

trainable=False,

initializer=tf.zeros_initializer())

v = tf.get_variable(

name=param_name + "/lamb_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

############## BELOW ARE THE SPECIFIC PARTS FOR LAMB ##############

# Note: Here are two choices for scaling function \phi(z)

# minmax: \phi(z) = min(max(z, \gamma_l), \gamma_u)

# identity: \phi(z) = z

# The authors does not mention what is \gamma_l and \gamma_u

# UPDATE: after asking authors, they provide me the code below.

# ratio = array_ops.where(math_ops.greater(w_norm, 0), array_ops.where(

# math_ops.greater(g_norm, 0), (w_norm / g_norm), 1.0), 1.0)

r1 = tf.sqrt(tf.reduce_sum(tf.square(param)))

r2 = tf.sqrt(tf.reduce_sum(tf.square(update)))

r = tf.where(tf.greater(r1, 0.0),

tf.where(tf.greater(r2, 0.0),

r1 / r2,

1.0),

1.0)

eta = self.learning_rate * r

update_with_lr = eta * 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