# tf.keras.optimizers.legacy.Ftrl

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|---|
| [![](https://www.tensorflow.org/images/GitHub-Mark-32px.png) View source on GitHub](https://github.com/keras-team/keras/tree/v2.13.1/keras/optimizers/legacy/ftrl.py#L26-L309) |

Optimizer that implements the FTRL algorithm.

Inherits From: [`Optimizer`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/keras/optimizers/legacy/Optimizer)

#### View aliases


**Main aliases**

[`tf.optimizers.legacy.Ftrl`](https://www.tensorflow.org/api_docs/python/tf/keras/optimizers/legacy/Ftrl)
**Compat aliases for migration**

See
[Migration guide](https://www.tensorflow.org/guide/migrate) for
more details.

\`tf.compat.v1.keras.optimizers.Ftrl\`, \`tf.compat.v1.keras.optimizers.legacy.Ftrl\`

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    tf.keras.optimizers.legacy.Ftrl(
        learning_rate=0.001,
        learning_rate_power=-0.5,
        initial_accumulator_value=0.1,
        l1_regularization_strength=0.0,
        l2_regularization_strength=0.0,
        name='Ftrl',
        l2_shrinkage_regularization_strength=0.0,
        beta=0.0,
        **kwargs
    )

"Follow The Regularized Leader" (FTRL) is an optimization algorithm
developed at Google for click-through rate prediction in the early 2010s. It
is most suitable for shallow models with large and sparse feature spaces.
The algorithm is described by
[McMahan et al., 2013](https://research.google.com/pubs/archive/41159.pdf).
The Keras version has support for both online L2 regularization
(the L2 regularization described in the paper
above) and shrinkage-type L2 regularization
(which is the addition of an L2 penalty to the loss function).

#### Initialization:

    n = 0
    sigma = 0
    z = 0

Update rule for one variable `w`:

    prev_n = n
    n = n + g ** 2
    sigma = (sqrt(n) - sqrt(prev_n)) / lr
    z = z + g - sigma * w
    if abs(z) < lambda_1:
      w = 0
    else:
      w = (sgn(z) * lambda_1 - z) / ((beta + sqrt(n)) / alpha + lambda_2)

#### Notation:

- `lr` is the learning rate
- `g` is the gradient for the variable
- `lambda_1` is the L1 regularization strength
- `lambda_2` is the L2 regularization strength

Check the documentation for the `l2_shrinkage_regularization_strength`
parameter for more details when shrinkage is enabled, in which case gradient
is replaced with a gradient with shrinkage.

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| ## Args ||
|---|---|
| `learning_rate` | A `Tensor`, floating point value, or a schedule that is a [`tf.keras.optimizers.schedules.LearningRateSchedule`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/keras/optimizers/schedules/LearningRateSchedule). The learning rate. |
| `learning_rate_power` | A float value, must be less or equal to zero. Controls how the learning rate decreases during training. Use zero for a fixed learning rate. |
| `initial_accumulator_value` | The starting value for accumulators. Only zero or positive values are allowed. |
| `l1_regularization_strength` | A float value, must be greater than or equal to zero. Defaults to `0.0`. |
| `l2_regularization_strength` | A float value, must be greater than or equal to zero. Defaults to `0.0`. |
| `name` | Optional name prefix for the operations created when applying gradients. Defaults to `"Ftrl"`. |
| `l2_shrinkage_regularization_strength` | A float value, must be greater than or equal to zero. This differs from L2 above in that the L2 above is a stabilization penalty, whereas this L2 shrinkage is a magnitude penalty. When input is sparse shrinkage will only happen on the active weights. |
| `beta` | A float value, representing the beta value from the paper. Defaults to `0.0`. |
| `**kwargs` | keyword arguments. Allowed arguments are `clipvalue`, `clipnorm`, `global_clipnorm`. If `clipvalue` (float) is set, the gradient of each weight is clipped to be no higher than this value. If `clipnorm` (float) is set, the gradient of each weight is individually clipped so that its norm is no higher than this value. If `global_clipnorm` (float) is set the gradient of all weights is clipped so that their global norm is no higher than this value. |

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| ## Reference ||
|---|---|
| <br /> - [McMahan et al., 2013](https://research.google.com/pubs/archive/41159.pdf) ||

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| ## Raises ||
|---|---|
| `ValueError` | in case of any invalid argument. |

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| ## Attributes ||
|---|---|
| `clipnorm` | `float` or `None`. If set, clips gradients to a maximum norm. |
| `clipvalue` | `float` or `None`. If set, clips gradients to a maximum value. |
| `global_clipnorm` | `float` or `None`. <br /> If set, clips gradients to a maximum norm. Check [`tf.clip_by_global_norm`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/clip_by_global_norm) for more details. |
| `iterations` | Variable. The number of training steps this Optimizer has run. |
| `weights` | Returns variables of this Optimizer based on the order created. |

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## Methods

### `add_slot`

[View source](https://github.com/keras-team/keras/tree/v2.13.1/keras/optimizers/legacy/optimizer_v2.py#L1021-L1084)

    add_slot(
        var, slot_name, initializer='zeros', shape=None
    )

Add a new slot variable for `var`.

A slot variable is an additional variable associated with `var` to
train. It is allocated and managed by optimizers, e.g. `Adam`.

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| Args ||
|---|---|
| `var` | a `Variable` object. |
| `slot_name` | name of the slot variable. |
| `initializer` | initializer of the slot variable |
| `shape` | (Optional) shape of the slot variable. If not set, it will default to the shape of `var`. |

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| Returns ||
|---|---|
| A slot variable. ||

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### `add_weight`

[View source](https://github.com/keras-team/keras/tree/v2.13.1/keras/optimizers/legacy/optimizer_v2.py#L1343-L1388)

    add_weight(
        name,
        shape,
        dtype=None,
        initializer='zeros',
        trainable=None,
        synchronization=https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/VariableSynchronization#AUTO,
        aggregation=https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/VariableAggregation#NONE
    )

### `apply_gradients`

[View source](https://github.com/keras-team/keras/tree/v2.13.1/keras/optimizers/legacy/optimizer_v2.py#L670-L767)

    apply_gradients(
        grads_and_vars, name=None, experimental_aggregate_gradients=True
    )

Apply gradients to variables.

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`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/distribute/Strategy) by default. You can aggregate gradients
yourself by passing `experimental_aggregate_gradients=False`.

#### Example:

    grads = tape.gradient(loss, vars)
    grads = tf.distribute.get_replica_context().all_reduce('sum', grads)
    # Processing aggregated gradients.
    optimizer.apply_gradients(zip(grads, vars),
        experimental_aggregate_gradients=False)

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| Args ||
|---|---|
| `grads_and_vars` | List of (gradient, variable) pairs. |
| `name` | Optional name for the returned operation. When `None`, uses the name passed to the `Optimizer` constructor. Defaults to `None`. |
| `experimental_aggregate_gradients` | Whether to sum gradients from different replicas in the presence of [`tf.distribute.Strategy`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/distribute/Strategy). If False, it's user responsibility to aggregate the gradients. Default to `True`. |

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

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| Raises ||
|---|---|
| `TypeError` | If `grads_and_vars` is malformed. |
| `ValueError` | If none of the variables have gradients. |
| `RuntimeError` | If called in a cross-replica context. |

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### `from_config`

[View source](https://github.com/keras-team/keras/tree/v2.13.1/keras/optimizers/legacy/optimizer_v2.py#L1216-L1240)

    @classmethod
    from_config(
        config, custom_objects=None
    )

Creates an optimizer from its config.

This method is the reverse of `get_config`,
capable of instantiating the same optimizer from the config
dictionary.

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| Args ||
|---|---|
| `config` | A Python dictionary, typically the output of get_config. |
| `custom_objects` | A Python dictionary mapping names to additional Python objects used to create this optimizer, such as a function used for a hyperparameter. |

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| Returns ||
|---|---|
| An optimizer instance. ||

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### `get_config`

[View source](https://github.com/keras-team/keras/tree/v2.13.1/keras/optimizers/legacy/ftrl.py#L287-L309)

    get_config()

Returns the config of the optimizer.

An optimizer config is a Python dictionary (serializable)
containing the configuration of an optimizer.
The same optimizer can be reinstantiated later
(without any saved state) from this configuration.

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| Returns ||
|---|---|
| Python dictionary. ||

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### `get_gradients`

[View source](https://github.com/keras-team/keras/tree/v2.13.1/keras/optimizers/legacy/optimizer_v2.py#L849-L879)

    get_gradients(
        loss, params
    )

Returns gradients of `loss` with respect to `params`.

Should be used only in legacy v1 graph mode.

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| Args ||
|---|---|
| `loss` | Loss tensor. |
| `params` | List of variables. |

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| Returns ||
|---|---|
| List of gradient tensors. ||

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| Raises ||
|---|---|
| `ValueError` | In case any gradient cannot be computed (e.g. if gradient function not implemented). |

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### `get_slot`

[View source](https://github.com/keras-team/keras/tree/v2.13.1/keras/optimizers/legacy/optimizer_v2.py#L1086-L1102)

    get_slot(
        var, slot_name
    )

### `get_slot_names`

[View source](https://github.com/keras-team/keras/tree/v2.13.1/keras/optimizers/legacy/optimizer_v2.py#L1017-L1019)

    get_slot_names()

A list of names for this optimizer's slots.

### `get_updates`

[View source](https://github.com/keras-team/keras/tree/v2.13.1/keras/optimizers/legacy/optimizer_v2.py#L881-L891)

    get_updates(
        loss, params
    )

### `get_weights`

[View source](https://github.com/keras-team/keras/tree/v2.13.1/keras/optimizers/legacy/optimizer_v2.py#L1263-L1290)

    get_weights()

Returns the current weights of the optimizer.

The weights of an optimizer are its state (ie, variables).
This function returns the weight values associated with this
optimizer as a list of Numpy arrays. The first value is always the
iterations count of the optimizer, followed by the optimizer's state
variables in the order they were created. The returned list can in turn
be used to load state into similarly parameterized optimizers.

For example, the RMSprop optimizer for this simple model returns a list
of three values-- the iteration count, followed by the root-mean-square
value of the kernel and bias of the single Dense layer:

    opt = tf.keras.optimizers.legacy.RMSprop()
    m = tf.keras.models.Sequential([tf.keras.layers.Dense(10)])
    m.compile(opt, loss='mse')
    data = np.arange(100).reshape(5, 20)
    labels = np.zeros(5)
    results = m.fit(data, labels)  # Training.
    len(opt.get_weights())
    3

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| Returns ||
|---|---|
| Weights values as a list of numpy arrays. ||

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### `minimize`

[View source](https://github.com/keras-team/keras/tree/v2.13.1/keras/optimizers/legacy/optimizer_v2.py#L567-L601)

    minimize(
        loss, var_list, grad_loss=None, name=None, tape=None
    )

Minimize `loss` by updating `var_list`.

This method simply computes gradient using [`tf.GradientTape`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/GradientTape) and calls
`apply_gradients()`. If you want to process the gradient before applying
then call [`tf.GradientTape`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/GradientTape) and `apply_gradients()` explicitly instead
of using this function.

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| Args ||
|---|---|
| `loss` | `Tensor` or callable. If a callable, `loss` should take no arguments and return the value to minimize. If a `Tensor`, the `tape` argument must be passed. |
| `var_list` | list or tuple of `Variable` objects to update to minimize `loss`, or a callable returning the list or tuple of `Variable` objects. Use callable when the variable list would otherwise be incomplete before `minimize` since the variables are created at the first time `loss` is called. |
| `grad_loss` | (Optional). A `Tensor` holding the gradient computed for `loss`. |
| `name` | (Optional) str. Name for the returned operation. |
| `tape` | (Optional) [`tf.GradientTape`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/GradientTape). If `loss` is provided as a `Tensor`, the tape that computed the `loss` must be provided. |

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| Returns ||
|---|---|
| An `Operation` that updates the variables in `var_list`. The `iterations` will be automatically increased by 1. ||

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| Raises ||
|---|---|
| `ValueError` | If some of the variables are not `Variable` objects. |

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### `set_weights`

[View source](https://github.com/keras-team/keras/tree/v2.13.1/keras/optimizers/legacy/optimizer_v2.py#L1293-L1341)

    set_weights(
        weights
    )

Set the weights of the optimizer.

The weights of an optimizer are its state (ie, variables).
This function takes the weight values associated with this
optimizer as a list of Numpy arrays. The first value is always the
iterations count of the optimizer, followed by the optimizer's state
variables in the order they are created. The passed values are used to
set the new state of the optimizer.

For example, the RMSprop optimizer for this simple model takes a list of
three values-- the iteration count, followed by the root-mean-square
value of the kernel and bias of the single Dense layer:

    opt = tf.keras.optimizers.legacy.RMSprop()
    m = tf.keras.models.Sequential([tf.keras.layers.Dense(10)])
    m.compile(opt, loss='mse')
    data = np.arange(100).reshape(5, 20)
    labels = np.zeros(5)
    results = m.fit(data, labels)  # Training.
    new_weights = [np.array(10), np.ones([20, 10]), np.zeros([10])]
    opt.set_weights(new_weights)
    opt.iterations
    <tf.Variable 'RMSprop/iter:0' shape=() dtype=int64, numpy=10>

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| Args ||
|---|---|
| `weights` | weight values as a list of numpy arrays. |

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### `variables`

[View source](https://github.com/keras-team/keras/tree/v2.13.1/keras/optimizers/legacy/optimizer_v2.py#L1254-L1256)

    variables()

Returns variables of this Optimizer based on the order created.