``````# Copyright 2015 The TensorFlow Authors. All Rights Reserved.
#
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#
# Unless required by applicable law or agreed to in writing, software
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# ==============================================================================

from __future__ import absolute_import
from __future__ import division
from __future__ import print_function

from tensorflow.python.framework import ops
from tensorflow.python.ops import control_flow_ops
from tensorflow.python.ops import math_ops
from tensorflow.python.ops import resource_variable_ops
from tensorflow.python.ops import state_ops
from tensorflow.python.ops import variable_scope
from tensorflow.python.training import optimizer
from tensorflow.python.training import training_ops

"""Optimizer that implements the Adam algorithm.

See [Kingma et al., 2014](http://arxiv.org/abs/1412.6980)
([pdf](http://arxiv.org/pdf/1412.6980.pdf)).
"""

def __init__(self, learning_rate=0.001, wdc = 0,  beta1=0.9, beta2=0.999, epsilon=1e-8,

Initialization:

```
m_0 <- 0 (Initialize initial 1st moment vector)
v_0 <- 0 (Initialize initial 2nd moment vector)
t <- 0 (Initialize timestep)
```

The update rule for `variable` with gradient `g` uses an optimization
described at the end of section2 of the paper:

```
t <- t + 1
lr_t <- learning_rate * sqrt(1 - beta2^t) / (1 - beta1^t)

m_t <- beta1 * m_{t-1} + (1 - beta1) * g
v_t <- beta2 * v_{t-1} + (1 - beta2) * g * g
variable <- variable - lr_t * m_t / (sqrt(v_t) + epsilon)
```

The default value of 1e-8 for epsilon might not be a good default in
general. For example, when training an Inception network on ImageNet a
current good choice is 1.0 or 0.1. Note that since AdamOptimizer uses the
formulation just before Section 2.1 of the Kingma and Ba paper rather than
the formulation in Algorithm 1, the "epsilon" referred to here is "epsilon
hat" in the paper.

The sparse implementation of this algorithm (used when the gradient is an
IndexedSlices object, typically because of `tf.gather` or an embedding
lookup in the forward pass) does apply momentum to variable slices even if
they were not used in the forward pass (meaning they have a gradient equal
to zero). Momentum decay (beta1) is also applied to the entire momentum
accumulator. This means that the sparse behavior is equivalent to the dense
behavior (in contrast to some momentum implementations which ignore momentum
unless a variable slice was actually used).

Args:
learning_rate: A Tensor or a floating point value.  The learning rate.
beta1: A float value or a constant float tensor.
The exponential decay rate for the 1st moment estimates.
beta2: A float value or a constant float tensor.
The exponential decay rate for the 2nd moment estimates.
epsilon: A small constant for numerical stability. This epsilon is
"epsilon hat" in the Kingma and Ba paper (in the formula just before
Section 2.1), not the epsilon in Algorithm 1 of the paper.
use_locking: If True use locks for update operations.
name: Optional name for the operations created when applying gradients.
"""
self._lr = learning_rate
self._beta1 = beta1
self._beta2 = beta2
self._epsilon = epsilon
self._wdc   = wdc

# Tensor versions of the constructor arguments, created in _prepare().
self._lr_t = None
self._beta1_t = None
self._beta2_t = None
self._epsilon_t = None
self._wdc_t = None

# Variables to accumulate the powers of the beta parameters.
# Created in _create_slots when we know the variables to optimize.
self._beta1_power = None
self._beta2_power = None

# Created in SparseApply if needed.
self._updated_lr = None

def _get_beta_accumulators(self):
return self._beta1_power, self._beta2_power

def _create_slots(self, var_list):
# Create the beta1 and beta2 accumulators on the same device as the first
# variable. Sort the var_list to make sure this device is consistent across
# workers (these need to go on the same PS, otherwise some updates are
# silently ignored).
first_var = min(var_list, key=lambda x: x.name)

if (self._beta1_power is None or
self._beta1_power.graph is not first_var.graph):
with ops.colocate_with(first_var):
self._beta1_power = variable_scope.variable(self._beta1,
name="beta1_power",
trainable=False)
self._beta2_power = variable_scope.variable(self._beta2,
name="beta2_power",
trainable=False)
# Create slots for the first and second moments.
for v in var_list:
self._zeros_slot(v, "m", self._name)
self._zeros_slot(v, "v", self._name)

def _prepare(self):
self._lr_t = ops.convert_to_tensor(self._lr, name="learning_rate")
self._beta1_t = ops.convert_to_tensor(self._beta1, name="beta1")
self._beta2_t = ops.convert_to_tensor(self._beta2, name="beta2")
self._epsilon_t = ops.convert_to_tensor(self._epsilon, name="epsilon")
self._wdc_t     = ops.convert_to_tensor(self._wdc, name="wdc")

m = self.get_slot(var, "m")
v = self.get_slot(var, "v")
var, m, v,
math_ops.cast(self._beta1_power, var.dtype.base_dtype),
math_ops.cast(self._beta2_power, var.dtype.base_dtype),
math_ops.cast(self._lr_t, var.dtype.base_dtype),
math_ops.cast(self._beta1_t, var.dtype.base_dtype),
math_ops.cast(self._beta2_t, var.dtype.base_dtype),
math_ops.cast(self._epsilon_t, var.dtype.base_dtype),

m = self.get_slot(var, "m")
v = self.get_slot(var, "v")
var.handle, m.handle, v.handle,

beta1_power = math_ops.cast(self._beta1_power, var.dtype.base_dtype)
beta2_power = math_ops.cast(self._beta2_power, var.dtype.base_dtype)
lr_t = math_ops.cast(self._lr_t, var.dtype.base_dtype)
beta1_t = math_ops.cast(self._beta1_t, var.dtype.base_dtype)
beta2_t = math_ops.cast(self._beta2_t, var.dtype.base_dtype)
epsilon_t = math_ops.cast(self._epsilon_t, var.dtype.base_dtype)
wdc_t  = math_ops.cast(self._wdc_t, var.dtype.base_dtype)

lr = (lr_t * math_ops.sqrt(1 - beta2_power) / (1 - beta1_power))

# m_t = beta1 * m + (1 - beta1) * g_t
m = self.get_slot(var, "m")
m_scaled_g_values = grad * (1 - beta1_t)
m_t = state_ops.assign(m, m * beta1_t,
use_locking=self._use_locking)
with ops.control_dependencies([m_t]):

# v_t = beta2 * v + (1 - beta2) * (g_t * g_t)
v = self.get_slot(var, "v")
v_t = state_ops.assign(v, v * beta2_t, use_locking=self._use_locking)
with ops.control_dependencies([v_t]):
v_sqrt = math_ops.sqrt(v_t)

#var_wdc = var - var * wdc_t
var_wdc  = state_ops.assign_sub(var,
var * wdc_t,
use_locking=self._use_locking)

var_update = state_ops.assign_sub(var_wdc,
lr * m_t / (v_sqrt + epsilon_t),
use_locking=self._use_locking)
return control_flow_ops.group(*[var_update, m_t, v_t])

return self._apply_sparse_shared(
lambda x, i, v: state_ops.scatter_add(  # pylint: disable=g-long-lambda
x, i, v, use_locking=self._use_locking))

with ops.control_dependencies(
x.handle, i, v)]):
return x.value()

return self._apply_sparse_shared(

def _finish(self, update_ops, name_scope):
# Update the power accumulators.
with ops.control_dependencies(update_ops):
with ops.colocate_with(self._beta1_power):
update_beta1 = self._beta1_power.assign(
self._beta1_power * self._beta1_t,
use_locking=self._use_locking)
update_beta2 = self._beta2_power.assign(
self._beta2_power * self._beta2_t,
use_locking=self._use_locking)
return control_flow_ops.group(*update_ops + [update_beta1, update_beta2],
name=name_scope)
``````