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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).


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

Update (


is variable index,


is the learning rate):

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

Check the documentation for the l2_shrinkage_regularization_strength parameter for more details when shrinkage is enabled, in which case gradient is replaced with 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.
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. When input is sparse shrinkage will only happen on the active weights.
beta A float value, representing the beta value from the paper.
**kwargs Keyword arguments. Allowed to be one of "clipnorm" or "clipvalue". "clipnorm" (float) clips gradients by norm; "clipvalue" (float) clips gradients by value.


ValueError in case of any invalid argument.