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Optimizer that implements the Adadelta algorithm.

Inherits From: Optimizer

Adadelta optimization is a stochastic gradient descent method that is based on adaptive learning rate per dimension to address two drawbacks:

1) the continual decay of learning rates throughout training 2) the need for a manually selected global learning rate

Two accumulation steps are required:

1) the accumulation of gradients squared, 2) the accumulation of updates squared.


$$E[g^2]_0 := 0 \text{(Initialize gradient 2nd order moment vector)}$$
$$E[\Delta x^2]_0 := 0 \text{(Initialize 2nd order variable update)}$$
$$t := t + 1$$
$$E[g^2]_t := \rho * E[g^2]_{t-1} + (1 - \rho) * g^2$$
$$\Delta x_t = -RMS[\Delta x]_{t-1} * g_t / RMS[g]_t$$
$$E[\Delta x^2]_t := \rho * E[\Delta x^2]_{t-1} + (1 - \rho) * \Delta x_t^2$$
$$x_t := x_{t-1} + \Delta x_{t}$$

References See M. D. Zeiler (pdf)

learning_rate A Tensor or a floating point value. The learning rate. To match the exact form in the original paper use 1.0.
rho A Tensor or a floating point value. The decay rate.
epsilon A Tensor or a floating point value. A constant epsilon used to better conditioning the grad update.
name Optional name prefix for the operations created when applying gradients. Defaults to "Adadelta".
**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.

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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Add a new slot variable for var.


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Apply gradients to variables.

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

grads_and_vars List of (gradient, variable) pairs.
name Optional name for the returned operation. Default to the name passed to the Optimizer constructor.

An Operation that applies the specified gradients. If global_step was not None, that operation also increments global_step.

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


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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.

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.

An optimizer instance.


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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.

Python dictionary.


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Returns gradients of loss with respect to params.

loss Loss tensor.
params List of variables.

List of gradient tensors.

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


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A list of names for this optimizer's slots.


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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.

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.

An Operation that updates the variables in var_list. If global_step was not None, that operation also increments global_step.

ValueError If some of the variables are not Variable objects.


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Returns variables of this Optimizer based on the order created.