Optimizer that implements the Adam algorithm.

Inherits From: `Optimizer`

### Used in the notebooks

Adam optimization is a stochastic gradient descent method that is based on adaptive estimation of first-order and second-order moments.

According to Kingma et al., 2014, the method is "computationally efficient, has little memory requirement, invariant to diagonal rescaling of gradients, and is well suited for problems that are large in terms of data/parameters".

`learning_rate` A `Tensor`, floating point value, or a schedule that is a `tf.keras.optimizers.schedules.LearningRateSchedule`, or a callable that takes no arguments and returns the actual value to use, The learning rate. Defaults to 0.001.
`beta_1` A float value or a constant float tensor, or a callable that takes no arguments and returns the actual value to use. The exponential decay rate for the 1st moment estimates. Defaults to 0.9.
`beta_2` A float value or a constant float tensor, or a callable that takes no arguments and returns the actual value to use, The exponential decay rate for the 2nd moment estimates. Defaults to 0.999.
`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. Defaults to 1e-7.
`amsgrad` Boolean. Whether to apply AMSGrad variant of this algorithm from the paper "On the Convergence of Adam and beyond". Defaults to `False`.
`name` Optional name for the operations created when applying gradients. Defaults to `"Adam"`.
`**kwargs` Keyword arguments. Allowed to be one of `"clipnorm"` or `"clipvalue"`. `"clipnorm"` (float) clips gradients by norm; `"clipvalue"` (float) clips gradients by value.

#### Usage:

````opt = tf.keras.optimizers.Adam(learning_rate=0.1)`
`var1 = tf.Variable(10.0)`
`loss = lambda: (var1 ** 2)/2.0       # d(loss)/d(var1) == var1`
`step_count = opt.minimize(loss, [var1]).numpy()`
`# The first step is `-learning_rate*sign(grad)``
`var1.numpy()`
`9.9`
```

#### Notes:

The default value of 1e-7 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 Adam 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).

`name` A non-empty string. The name to use for accumulators created for the optimizer.
`**kwargs` keyword arguments. Allowed to be {`clipnorm`, `clipvalue`, `lr`, `decay`}. `clipnorm` is clip gradients by norm; `clipvalue` is clip gradients by value, `decay` is included for backward compatibility to allow time inverse decay of learning rate. `lr` is included for backward compatibility, recommended to use `learning_rate` instead.

`ValueError` If name is malformed.

`iterations` Variable. The number of training steps this Optimizer has run.
`weights` Returns variables of this Optimizer based on the order created.

## Methods

### `add_slot`

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Add a new slot variable for `var`.

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### `apply_gradients`

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This is the second part of `minimize()`. It returns an `Operation` that applies gradients.

The method sums gradients from all replicas in the presence of `tf.distribute.Strategy` by default. You can aggregate gradients yourself by passing `experimental_aggregate_gradients=False`.

#### Example:

``````grads = tape.gradient(loss, vars)

``````

Args
`grads_and_vars` List of (gradient, variable) pairs.
`name` Optional name for the returned operation. Default to the name passed to the `Optimizer` constructor.
`experimental_aggregate_gradients` Whether to sum gradients from different replicas in the presense of `tf.distribute.Strategy`. If False, it's user responsibility to aggregate the gradients. Default to True.

Returns
An `Operation` that applies the specified gradients. The `iterations` will be automatically increased by 1.

Raises
`TypeError` If `grads_and_vars` is malformed.
`ValueErro`