Maintains moving averages of variables by employing an exponential decay.

When training a model, it is often beneficial to maintain moving averages of
the trained parameters.  Evaluations that use averaged parameters sometimes
produce significantly better results than the final trained values.

The `apply()` method adds shadow copies of trained variables and add ops that
maintain a moving average of the trained variables in their shadow copies.
It is used when building the training model.  The ops that maintain moving
averages are typically run after each training step.
The `average()` and `average_name()` methods give access to the shadow
variables and their names.  They are useful when building an evaluation
model, or when restoring a model from a checkpoint file.  They help use the
moving averages in place of the last trained values for evaluations.

The moving averages are computed using exponential decay.  You specify the
decay value when creating the `ExponentialMovingAverage` object.  The shadow
variables are initialized with the same initial values as the trained
variables.  When you run the ops to maintain the moving averages, each
shadow variable is updated with the formula:

  `shadow_variable -= (1 - decay) * (shadow_variable - variable)`

This is mathematically equivalent to the classic formula below, but the use
of an `assign_sub` op (the `"-="` in the formula) allows concurrent lockless
updates to the variables:

  `shadow_variable = decay * shadow_variable + (1 - decay) * variable`

Reasonable values for `decay` are close to 1.0, typically in the
multiple-nines range: 0.999, 0.9999, etc.

Example usage when creating a training model:

```python
# Create variables.
var0 = tf.Variable(...)
var1 = tf.Variable(...)
# ... use the variables to build a training model...
...
# Create an op that applies the optimizer.  This is what we usually
# would use as a training op.
opt_op = opt.minimize(my_loss, [var0, var1])

# Create an ExponentialMovingAverage object
ema = tf.train.ExponentialMovingAverage(decay=0.9999)

# Create the shadow variables, and add ops to maintain moving averages
# of var0 and var1.
maintain_averages_op = ema.apply([var0, var1])

# Create an op that will update the moving averages after each training
# step.  This is what we will use in place of the usual training op.
with tf.control_dependencies([opt_op]):
    training_op = tf.group(maintain_averages_op)

...train the model by running training_op...
```

There are two ways to use the moving averages for evaluations:

*  Build a model that uses the shadow variables instead of the variables.
   For this, use the `average()` method which returns the shadow variable
   for a given variable.
*  Build a model normally but load the checkpoint files to evaluate by using
   the shadow variable names.  For this use the `average_name()` method.  See
   the [Saver class](../../api_docs/python/train.md#Saver) for more
   information on restoring saved variables.

Example of restoring the shadow variable values:

```python
# Create a Saver that loads variables from their saved shadow values.
shadow_var0_name = ema.average_name(var0)
shadow_var1_name = ema.average_name(var1)
saver = tf.train.Saver({shadow_var0_name: var0, shadow_var1_name: var1})
saver.restore(...checkpoint filename...)
# var0 and var1 now hold the moving average values
```

- - -

#### `tf.train.ExponentialMovingAverage.__init__(decay, num_updates=None, name='ExponentialMovingAverage')` {#ExponentialMovingAverage.__init__}

Creates a new ExponentialMovingAverage object.

The `apply()` method has to be called to create shadow variables and add
ops to maintain moving averages.

The optional `num_updates` parameter allows one to tweak the decay rate
dynamically. It is typical to pass the count of training steps, usually
kept in a variable that is incremented at each step, in which case the
decay rate is lower at the start of training.  This makes moving averages
move faster.  If passed, the actual decay rate used is:

  `min(decay, (1 + num_updates) / (10 + num_updates))`

##### Args:


*  <b>`decay`</b>: Float.  The decay to use.
*  <b>`num_updates`</b>: Optional count of number of updates applied to variables.
*  <b>`name`</b>: String. Optional prefix name to use for the name of ops added in
    `apply()`.


- - -

#### `tf.train.ExponentialMovingAverage.apply(var_list=None)` {#ExponentialMovingAverage.apply}

Maintains moving averages of variables.

`var_list` must be a list of `Variable` or `Tensor` objects.  This method
creates shadow variables for all elements of `var_list`.  Shadow variables
for `Variable` objects are initialized to the variable's initial value.
They will be added to the `GraphKeys.MOVING_AVERAGE_VARIABLES` collection.
For `Tensor` objects, the shadow variables are initialized to 0 and zero
debiased (see docstring in `assign_moving_average` for more details).

shadow variables are created with `trainable=False` and added to the
`GraphKeys.ALL_VARIABLES` collection.  They will be returned by calls to
`tf.all_variables()`.

Returns an op that updates all shadow variables as described above.

Note that `apply()` can be called multiple times with different lists of
variables.

##### Args:


*  <b>`var_list`</b>: A list of Variable or Tensor objects. The variables
    and Tensors must be of types float16, float32, or float64.

##### Returns:

  An Operation that updates the moving averages.

##### Raises:


*  <b>`TypeError`</b>: If the arguments are not all float16, float32, or float64.
*  <b>`ValueError`</b>: If the moving average of one of the variables is already
    being computed.


- - -

#### `tf.train.ExponentialMovingAverage.average_name(var)` {#ExponentialMovingAverage.average_name}

Returns the name of the `Variable` holding the average for `var`.

The typical scenario for `ExponentialMovingAverage` is to compute moving
averages of variables during training, and restore the variables from the
computed moving averages during evaluations.

To restore variables, you have to know the name of the shadow variables.
That name and the original variable can then be passed to a `Saver()` object
to restore the variable from the moving average value with:
  `saver = tf.train.Saver({ema.average_name(var): var})`

`average_name()` can be called whether or not `apply()` has been called.

##### Args:


*  <b>`var`</b>: A `Variable` object.

##### Returns:

  A string: The name of the variable that will be used or was used
  by the `ExponentialMovingAverage class` to hold the moving average of
  `var`.


- - -

#### `tf.train.ExponentialMovingAverage.average(var)` {#ExponentialMovingAverage.average}

Returns the `Variable` holding the average of `var`.

##### Args:


*  <b>`var`</b>: A `Variable` object.

##### Returns:

  A `Variable` object or `None` if the moving average of `var`
  is not maintained.


- - -

#### `tf.train.ExponentialMovingAverage.variables_to_restore(moving_avg_variables=None)` {#ExponentialMovingAverage.variables_to_restore}

Returns a map of names to `Variables` to restore.

If a variable has a moving average, use the moving average variable name as
the restore name; otherwise, use the variable name.

For example,

```python
  variables_to_restore = ema.variables_to_restore()
  saver = tf.train.Saver(variables_to_restore)
```

Below is an example of such mapping:

```
  conv/batchnorm/gamma/ExponentialMovingAverage: conv/batchnorm/gamma,
  conv_4/conv2d_params/ExponentialMovingAverage: conv_4/conv2d_params,
  global_step: global_step
```

##### Args:


*  <b>`moving_avg_variables`</b>: a list of variables that require to use of the
    moving variable name to be restored. If None, it will default to
    variables.moving_average_variables() + variables.trainable_variables()

##### Returns:

  A map from restore_names to variables. The restore_name can be the
  moving_average version of the variable name if it exist, or the original
  variable name.


