# tf.keras.optimizers.Ftrl

Optimizer that implements the FTRL algorithm.

Inherits From: `Optimizer`

"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. 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.

`learning_rate` A `Tensor`, floating point value, or a schedule that is a `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 to be one of `"clipnorm"` or `"clipvalue"`. `"clipnorm"` (float) clips gradients by norm; `"clipvalue"` (float) clips gradients by value.

#### Reference:

`ValueError` in case of any invalid argument.

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