class_docstr: Optimizer that implements the Adam algorithm.
  
  References:
    Adam - A Method for Stochastic Optimization:
      [Kingma et al., 2015](https://arxiv.org/abs/1412.6980)
      ([pdf](https://arxiv.org/pdf/1412.6980.pdf))
  
  @compatibility(TF2)
  tf.compat.v1.train.AdamOptimizer is compatible with eager mode and
  `tf.function`.
  When eager execution is enabled, `learning_rate`, `beta1`, `beta2`, and
  `epsilon` can each be a callable that takes no arguments and returns the
  actual value to use. This can be useful for changing these values across
  different invocations of optimizer functions.
  
  To switch to native TF2 style, use [`tf.keras.optimizers.Adam`]
  (https://www.tensorflow.org/api_docs/python/tf/keras/optimizers/Adam)
  instead. Please notice that due to the implementation differences,
  `tf.keras.optimizers.Adam` and
  `tf.compat.v1.train.AdamOptimizer` may have slight differences in
  floating point numerics even though the formula used for the variable
  updates still matches.
  
  #### Structural Mapping to Native TF2
  
  Before:
  
  ```python
  optimizer = tf.compat.v1.train.AdamOptimizer(learning_rate=0.001)
  ```
  
  After:
  
  ```python
  optimizer = tf.keras.optimizers.Adam(learning_rate=0.001)
  ```
  
  #### How to Map Arguments
  |TF1 Arg Name          |TF2 Arg Name |Note                  |
  |----------------------|-------------|----------------------|
  |learning_rate         |learning_rate|Be careful of setting learning_rate as a
  :                      :             : tensor value computed from the global
  :                      :             : step. In TF1 this was usually meant to
  :                      :             : imply a dynamic learning rate and would
  :                      :             : recompute in each step. In TF2 (eager +
  :                      :             : function) it will treat it as a scalar
  :                      :             : value that only gets computed once
  :                      :             : instead of a symbolic placeholder to be
  :                      :             : computed each time.                   :
  |beta1                 |beta_1        |                      |
  |beta2                 |beta_2        |                      |
  |epsilon               |epsilon      | Default value is 1e-08 in TF1, but
  :                      :             : 1e-07 in TF2.                     :
  |use_locking           |N/A          |Not applicable in TF2. |
  
  #### Before & After Usage Example
  Before:
  
  ```python
  x = tf.Variable([1,2,3], dtype=tf.float32)
  grad = tf.constant([0.1, 0.2, 0.3])
  optimizer = tf.compat.v1.train.AdamOptimizer(learning_rate=0.001)
  optimizer.apply_gradients(zip([grad], [x]))
  ```
  
  After:
  
  ```python
  x = tf.Variable([1,2,3], dtype=tf.float32)
  grad = tf.constant([0.1, 0.2, 0.3])
  optimizer = tf.keras.optimizers.Adam(learning_rate=0.001)
  optimizer.apply_gradients(zip([grad], [x]))
  ```
  
  @end_compatibility
docstr: Construct a new Adam optimizer.
  
  Initialization:
  
  $$m_0 := 0 \text{(Initialize initial 1st moment vector)}$$
  $$v_0 := 0 \text{(Initialize initial 2nd moment vector)}$$
  $$t := 0 \text{(Initialize timestep)}$$
  
  The update rule for `variable` with gradient `g` uses an optimization
  described at the end of section 2 of the paper:
  
  $$t := t + 1$$
  $$\text{lr}_t := \mathrm{learning_rate} *
    \sqrt{1 - \beta_2^t} / (1 - \beta_1^t)$$
  
  $$m_t := \beta_1 * m_{t-1} + (1 - \beta_1) * g$$
  $$v_t := \beta_2 * v_{t-1} + (1 - \beta_2) * g * g$$
  $$\text{variable} := \text{variable} -
    \text{lr}_t * m_t / (\sqrt{v_t} + \epsilon)$$
  
  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.
      Defaults to "Adam".
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code: def __init__(
      self,
      learning_rate=0.001,
      beta1=0.9,
      beta2=0.999,
      epsilon=1e-8,
      use_locking=False,
      name="Adam",
  ):
      r"""Construct a new Adam optimizer.
  
      Initialization:
  
      $$m_0 := 0 \text{(Initialize initial 1st moment vector)}$$
      $$v_0 := 0 \text{(Initialize initial 2nd moment vector)}$$
      $$t := 0 \text{(Initialize timestep)}$$
  
      The update rule for `variable` with gradient `g` uses an optimization
      described at the end of section 2 of the paper:
  
      $$t := t + 1$$
      $$\text{lr}_t := \mathrm{learning_rate} *
        \sqrt{1 - \beta_2^t} / (1 - \beta_1^t)$$
  
      $$m_t := \beta_1 * m_{t-1} + (1 - \beta_1) * g$$
      $$v_t := \beta_2 * v_{t-1} + (1 - \beta_2) * g * g$$
      $$\text{variable} := \text{variable} -
        \text{lr}_t * m_t / (\sqrt{v_t} + \epsilon)$$
  
      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.
          Defaults to "Adam".
  
  
      """
  
      super(AdamOptimizer, self).__init__(use_locking, name)
      self._lr = learning_rate
      self._beta1 = beta1
      self._beta2 = beta2
      self._epsilon = epsilon
  
      # 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
  
imports: from tensorflow.python.eager import context
  from tensorflow.python.framework import ops
  from tensorflow.python.ops import control_flow_ops
  from tensorflow.python.ops import gen_training_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.training import optimizer
  from tensorflow.python.util.tf_export import tf_export
label_desc: Use image node_id 1 to create a new AdamOptimizer object from inherited base classes: optimizer with example: obj = AdamOptimizer(learning_rate, beta1, beta2, epsilon, use_locking, name)