Adadelta is an optimizer that uses two ideas to improve upon the two main drawbacks of the Adagrad method: More...

Public Member Functions
	AdaDelta (DecomposableFunctionType &function, const double rho=0.95, const double eps=1e-6, const size_t maxIterations=100000, const double tolerance=1e-5, const bool shuffle=true)
	Construct the AdaDelta optimizer with the given function and parameters. More...

double	Epsilon () const
	Get the value used to initialise the mean squared gradient parameter. More...

double &	Epsilon ()
	Modify the value used to initialise the mean squared gradient parameter. More...

const DecomposableFunctionType &	Function () const
	Get the instantiated function to be optimized. More...

DecomposableFunctionType &	Function ()
	Modify the instantiated function. More...

size_t	MaxIterations () const
	Get the maximum number of iterations (0 indicates no limit). More...

size_t &	MaxIterations ()
	Modify the maximum number of iterations (0 indicates no limit). More...

double	Optimize (arma::mat &iterate)
	Optimize the given function using AdaDelta. More...

double	Rho () const
	Get the smoothing parameter. More...

double &	Rho ()
	Modify the smoothing parameter. More...

bool	Shuffle () const
	Get whether or not the individual functions are shuffled. More...

bool &	Shuffle ()
	Modify whether or not the individual functions are shuffled. More...

double	Tolerance () const
	Get the tolerance for termination. More...

double &	Tolerance ()
	Modify the tolerance for termination. More...

Private Attributes
double	eps
	The value used to initialise the mean squared gradient parameter. More...

DecomposableFunctionType &	function
	The instantiated function. More...

size_t	maxIterations
	The maximum number of allowed iterations. More...

double	rho
	The smoothing parameter. More...

bool	shuffle
	Controls whether or not the individual functions are shuffled when iterating. More...

double	tolerance
	The tolerance for termination. More...

Detailed Description

template<typename DecomposableFunctionType>
class mlpack::optimization::AdaDelta< DecomposableFunctionType >

Adadelta is an optimizer that uses two ideas to improve upon the two main drawbacks of the Adagrad method:

Accumulate Over Window
Correct Units with Hessian Approximation

For more information, see the following.

@article{Zeiler2012,
  author    = {Matthew D. Zeiler},
  title     = {{ADADELTA:} An Adaptive Learning Rate Method},
  journal   = {CoRR},
  year      = {2012}
}

For AdaDelta to work, a DecomposableFunctionType template parameter is required. This class must implement the following function:

size_t NumFunctions(); double Evaluate(const arma::mat& coordinates, const size_t i); void Gradient(const arma::mat& coordinates, const size_t i, arma::mat& gradient);

NumFunctions() should return the number of functions ( $n$ ), and in the other two functions, the parameter i refers to which individual function (or gradient) is being evaluated. So, for the case of a data-dependent function, such as NCA (see mlpack::nca::NCA), NumFunctions() should return the number of points in the dataset, and Evaluate(coordinates, 0) will evaluate the objective function on the first point in the dataset (presumably, the dataset is held internally in the DecomposableFunctionType).

Template Parameters

DecomposableFunctionType Decomposable objective function type to be minimized.

Definition at line 63 of file ada_delta.hpp.

Constructor & Destructor Documentation

template<typename DecomposableFunctionType >

mlpack::optimization::AdaDelta< DecomposableFunctionType >::AdaDelta	(	DecomposableFunctionType &	function,
		const double	rho = `0.95`,
		const double	eps = `1e-6`,
		const size_t	maxIterations = `100000`,
		const double	tolerance = `1e-5`,
		const bool	shuffle = `true`
	)

Construct the AdaDelta optimizer with the given function and parameters.

The defaults here are not necessarily good for the given problem, so it is suggested that the values used be tailored to the task at hand. The maximum number of iterations refers to the maximum number of points that are processed (i.e., one iteration equals one point; one iteration does not equal one pass over the dataset).

Parameters

function	Function to be optimized (minimized).
rho	Smoothing constant
eps	Value used to initialise the mean squared gradient parameter.
maxIterations	Maximum number of iterations allowed (0 means no limit).
tolerance	Maximum absolute tolerance to terminate algorithm.
shuffle	If true, the function order is shuffled; otherwise, each function is visited in linear order.

Member Function Documentation

template<typename DecomposableFunctionType >

double mlpack::optimization::AdaDelta< DecomposableFunctionType >::Epsilon ( ) const

inline

Get the value used to initialise the mean squared gradient parameter.

Definition at line 111 of file ada_delta.hpp.

References mlpack::optimization::AdaDelta< DecomposableFunctionType >::eps.

template<typename DecomposableFunctionType >

double& mlpack::optimization::AdaDelta< DecomposableFunctionType >::Epsilon ( )

inline

Modify the value used to initialise the mean squared gradient parameter.

Definition at line 113 of file ada_delta.hpp.

References mlpack::optimization::AdaDelta< DecomposableFunctionType >::eps.

template<typename DecomposableFunctionType >

const DecomposableFunctionType& mlpack::optimization::AdaDelta< DecomposableFunctionType >::Function ( ) const

inline

Get the instantiated function to be optimized.

Definition at line 101 of file ada_delta.hpp.

template<typename DecomposableFunctionType >

DecomposableFunctionType& mlpack::optimization::AdaDelta< DecomposableFunctionType >::Function ( )

inline

Modify the instantiated function.

Definition at line 103 of file ada_delta.hpp.

template<typename DecomposableFunctionType >

size_t mlpack::optimization::AdaDelta< DecomposableFunctionType >::MaxIterations ( ) const

inline

Get the maximum number of iterations (0 indicates no limit).

Definition at line 116 of file ada_delta.hpp.

References mlpack::optimization::AdaDelta< DecomposableFunctionType >::maxIterations.

template<typename DecomposableFunctionType >

size_t& mlpack::optimization::AdaDelta< DecomposableFunctionType >::MaxIterations ( )

inline

Modify the maximum number of iterations (0 indicates no limit).

Definition at line 118 of file ada_delta.hpp.

References mlpack::optimization::AdaDelta< DecomposableFunctionType >::maxIterations.

template<typename DecomposableFunctionType >

double mlpack::optimization::AdaDelta< DecomposableFunctionType >::Optimize ( arma::mat & iterate )

Optimize the given function using AdaDelta.

The given starting point will be modified to store the finishing point of the algorithm, and the final objective value is returned.

Parameters

iterate Starting point (will be modified).

Returns: Objective value of the final point.

template<typename DecomposableFunctionType >

double mlpack::optimization::AdaDelta< DecomposableFunctionType >::Rho ( ) const

inline

Get the smoothing parameter.

Definition at line 106 of file ada_delta.hpp.

References mlpack::optimization::AdaDelta< DecomposableFunctionType >::rho.

template<typename DecomposableFunctionType >

double& mlpack::optimization::AdaDelta< DecomposableFunctionType >::Rho ( )

inline

Modify the smoothing parameter.

Definition at line 108 of file ada_delta.hpp.

References mlpack::optimization::AdaDelta< DecomposableFunctionType >::rho.

template<typename DecomposableFunctionType >

bool mlpack::optimization::AdaDelta< DecomposableFunctionType >::Shuffle ( ) const

inline

Get whether or not the individual functions are shuffled.

Definition at line 126 of file ada_delta.hpp.

References mlpack::optimization::AdaDelta< DecomposableFunctionType >::shuffle.

template<typename DecomposableFunctionType >

bool& mlpack::optimization::AdaDelta< DecomposableFunctionType >::Shuffle ( )

inline

Modify whether or not the individual functions are shuffled.

Definition at line 128 of file ada_delta.hpp.

References mlpack::optimization::AdaDelta< DecomposableFunctionType >::shuffle.

template<typename DecomposableFunctionType >

double mlpack::optimization::AdaDelta< DecomposableFunctionType >::Tolerance ( ) const

inline

Get the tolerance for termination.

Definition at line 121 of file ada_delta.hpp.

References mlpack::optimization::AdaDelta< DecomposableFunctionType >::tolerance.

template<typename DecomposableFunctionType >

double& mlpack::optimization::AdaDelta< DecomposableFunctionType >::Tolerance ( )

inline

Modify the tolerance for termination.

Definition at line 123 of file ada_delta.hpp.

References mlpack::optimization::AdaDelta< DecomposableFunctionType >::tolerance.

Member Data Documentation

template<typename DecomposableFunctionType >

double mlpack::optimization::AdaDelta< DecomposableFunctionType >::eps

private

The value used to initialise the mean squared gradient parameter.

Definition at line 138 of file ada_delta.hpp.

Referenced by mlpack::optimization::AdaDelta< DecomposableFunctionType >::Epsilon().

template<typename DecomposableFunctionType >

DecomposableFunctionType& mlpack::optimization::AdaDelta< DecomposableFunctionType >::function

private

The instantiated function.

Definition at line 132 of file ada_delta.hpp.

template<typename DecomposableFunctionType >

size_t mlpack::optimization::AdaDelta< DecomposableFunctionType >::maxIterations

private

The maximum number of allowed iterations.

Definition at line 141 of file ada_delta.hpp.

Referenced by mlpack::optimization::AdaDelta< DecomposableFunctionType >::MaxIterations().

template<typename DecomposableFunctionType >

double mlpack::optimization::AdaDelta< DecomposableFunctionType >::rho

private

The smoothing parameter.

Definition at line 135 of file ada_delta.hpp.

Referenced by mlpack::optimization::AdaDelta< DecomposableFunctionType >::Rho().

template<typename DecomposableFunctionType >

bool mlpack::optimization::AdaDelta< DecomposableFunctionType >::shuffle

private

Controls whether or not the individual functions are shuffled when iterating.

Definition at line 148 of file ada_delta.hpp.

Referenced by mlpack::optimization::AdaDelta< DecomposableFunctionType >::Shuffle().

template<typename DecomposableFunctionType >

double mlpack::optimization::AdaDelta< DecomposableFunctionType >::tolerance

private

The tolerance for termination.

Definition at line 144 of file ada_delta.hpp.

Referenced by mlpack::optimization::AdaDelta< DecomposableFunctionType >::Tolerance().

The documentation for this class was generated from the following file:

src/mlpack/core/optimizers/adadelta/ada_delta.hpp

Public Member Functions

Private Attributes

Detailed Description

template<typename DecomposableFunctionType> class mlpack::optimization::AdaDelta< DecomposableFunctionType >

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

template<typename DecomposableFunctionType>
class mlpack::optimization::AdaDelta< DecomposableFunctionType >