# tf.keras.optimizers.Ftrl

Optimizer that implements the FTRL algorithm.

Inherits From: Optimizer

See Algorithm 1 of this paper. This version has support for both online L2 (the L2 penalty given in the paper above) and shrinkage-type L2 (which is the addition of an L2 penalty to the loss function).

#### Initialization:

$$t = 0$$
$$n_{0} = 0$$
$$\sigma_{0} = 0$$
$$z_{0} = 0$$

Update (

$$i$$

is variable index):

$$t = t + 1$$
$$n_{t,i} = n_{t-1,i} + g_{t,i}^{2}$$
$$\sigma_{t,i} = (\sqrt{n_{t,i} } - \sqrt{n_{t-1,i} }) / \alpha$$
$$z_{t,i} = z_{t-1,i} + g_{t,i} - \sigma_{t,i} * w_{t,i}$$
$$w_{t,i} = - ((\beta+\sqrt{n+{t} }) / \alpha + \lambda_{2})^{-1} * (z_{i} - sgn(z_{i}) * \lambda_{1}) if \abs{z_{i} } > \lambda_{i} else 0$$

Check the documentation for the l2_shrinkage_regularization_strength parameter for more details when shrinkage is enabled, where gradient is replaced with gradient_with_shrinkage.

learning_rate A float value or a constant float Tensor.
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.
l2_regularization_strength A float value, must be greater than or equal to zero.
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. The FTRL formulation can be written as: w_{t+1} = argminw(\hat{g}{1:t}w + L1||w||_1 + L2||w||_2^2), where \hat{g} = g + (2L2_shrinkagew), and g is the gradient of the loss function w.r.t. the weights w. Specifically, in the absence of L1 regularization, it is equivalent to the following update rule: w_{t+1} = w_t - lr_t / (1 + 2L2lr_t) * g_t - 2L2_shrinkagelr_t / (1 + 2L2lr_t) * w_t where lr_t is the learning rate at t. When input is sparse shrinkage will only happen on the active weights.
**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 one of the arguments is invalid.

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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Apply gradients to variables.

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

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.

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

Raises
TypeError If grads_and_vars is malformed.
ValueError If none of the variables have gradients.

### from_config

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Creates an optimizer from its config.

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

Arguments
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.

Returns
An optimizer instance.

### get_config

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Returns the config of the optimimizer.

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.

Returns
Python dictionary.

### get_gradients

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Returns gradients of loss with respect to params.

Arguments
loss Loss tensor.
params List of variables.

Returns
List of gradient tensors.

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

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### get_slot_names

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A list of names for this optimizer's slots.

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### minimize

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Minimize loss by updating var_list.

This method simply computes gradient using tf.GradientTape and calls apply_gradients(). If you want to process the gradient before applying then call tf.GradientTape and apply_gradients() explicitly instead of using this function.

Args
loss A callable taking no arguments which returns the value to minimize.
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 name for the returned operation.

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

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

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### variables

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Returns variables of this Optimizer based on the order created.

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