This class offers methods for the usage of the Resilient-Backpropagation-algorithm with/out weight-backtracking. More...

#include <shark/Algorithms/GradientDescent/Rprop.h>

Inheritance diagram for shark::Rprop< SearchPointType >:

Public Types
typedef AbstractObjectiveFunction< SearchPointType, double >	ObjectiveFunctionType

Public Types inherited from shark::AbstractSingleObjectiveOptimizer< PointType >
typedef base_type::SearchPointType	SearchPointType

typedef base_type::SolutionType	SolutionType

typedef base_type::ResultType	ResultType

typedef base_type::ObjectiveFunctionType	ObjectiveFunctionType

Public Types inherited from shark::AbstractOptimizer< PointType, double, SingleObjectiveResultSet< PointType > >
enum	Feature
	Models features that the optimizer requires from the objective function. More...

typedef PointType	SearchPointType

typedef double	ResultType

typedef SingleObjectiveResultSet< PointType >	SolutionType

typedef AbstractObjectiveFunction< PointType, ResultType >	ObjectiveFunctionType

typedef TypedFlags< Feature >	Features

typedef TypedFeatureNotAvailableException< Feature >	FeatureNotAvailableException

Public Member Functions
	Rprop ()

std::string	name () const
	From INameable: return the class name.

void	init (ObjectiveFunctionType const &objectiveFunction, SearchPointType const &startingPoint)

void	init (ObjectiveFunctionType const &objectiveFunction, SearchPointType const &startingPoint, double initDelta)

void	step (ObjectiveFunctionType const &objectiveFunction)

virtual void	read (InArchive &archive)
	Read the component from the supplied archive.

virtual void	write (OutArchive &archive) const
	Write the component to the supplied archive.

void	setEtaMinus (double etaMinus)
	set decrease factor

void	setEtaPlus (double etaPlus)
	set increase factor

void	setMaxDelta (double d)
	set upper limit on update

void	setMinDelta (double d)
	set lower limit on update

void	setUseOldValue (bool useOldValue)

void	setUseFreezing (bool useFreezing)

void	setUseBacktracking (bool useBacktracking)

double	maxDelta () const
	return the maximal step size component

SearchPointType const &	derivative () const
	Returns the derivative at the current point. Can be used for stopping criteria.

Public Member Functions inherited from shark::AbstractSingleObjectiveOptimizer< PointType >
std::size_t	numInitPoints () const
	By default most single objective optimizers only require a single point.

virtual void	init (ObjectiveFunctionType const &function, std::vector< SearchPointType > const &initPoints)
	Initialize the optimizer for the supplied objective function using a set of initialisation points.

virtual void	init (ObjectiveFunctionType const &function, SearchPointType const &startingPoint)=0
	initializes the optimizer using a predefined starting point

virtual const SolutionType &	solution () const
	returns the current solution of the optimizer

Public Member Functions inherited from shark::AbstractOptimizer< PointType, double, SingleObjectiveResultSet< PointType > >
const Features &	features () const

virtual void	updateFeatures ()

bool	requiresValue () const

bool	requiresFirstDerivative () const

bool	requiresSecondDerivative () const

bool	canSolveConstrained () const

bool	requiresClosestFeasible () const

virtual	~AbstractOptimizer ()

virtual void	init (ObjectiveFunctionType const &function)
	Initialize the optimizer for the supplied objective function.

virtual void	step (ObjectiveFunctionType const &function)=0
	Carry out one step of the optimizer for the supplied objective function.

Public Member Functions inherited from shark::INameable
virtual	~INameable ()

Public Member Functions inherited from shark::ISerializable
virtual	~ISerializable ()
	Virtual d'tor.

void	load (InArchive &archive, unsigned int version)
	Versioned loading of components, calls read(...).

void	save (OutArchive &archive, unsigned int version) const
	Versioned storing of components, calls write(...).

	BOOST_SERIALIZATION_SPLIT_MEMBER ()

Protected Attributes
SearchPointType	m_derivative

double	m_increaseFactor
	The increase factor \( \eta^+ \), set to 1.2 by default.

double	m_decreaseFactor
	The decrease factor \( \eta^- \), set to 0.5 by default.

double	m_maxDelta
	The upper limit of the increments \( \Delta w_i^{(t)} \), set to 1e100 by default.

double	m_minDelta
	The lower limit of the increments \( \Delta w_i^{(t)} \), set to 0.0 by default.

double	m_oldValue
	The last function value observed.

size_t	m_parameterSize

SearchPointType	m_oldDerivative
	The last error gradient.

SearchPointType	m_deltaw
	the step eprformed last. used for weight backtracking

SearchPointType	m_delta
	The absolute update values (increment) for all weights.

bool	m_useFreezing

bool	m_useBacktracking

bool	m_useOldValue

Protected Attributes inherited from shark::AbstractSingleObjectiveOptimizer< PointType >
SolutionType	m_best
	Current solution of the optimizer.

Protected Attributes inherited from shark::AbstractOptimizer< PointType, double, SingleObjectiveResultSet< PointType > >
Features	m_features

Additional Inherited Members
Protected Member Functions inherited from shark::AbstractOptimizer< PointType, double, SingleObjectiveResultSet< PointType > >
void	checkFeatures (ObjectiveFunctionType const &objectiveFunction)
	Convenience function that checks whether the features of the supplied objective function match with the required features of the optimizer.

Detailed Description

template<class SearchPointType = RealVector>
class shark::Rprop< SearchPointType >

This class offers methods for the usage of the Resilient-Backpropagation-algorithm with/out weight-backtracking.

The Rprop algorithm is an improvement of the algorithms with adaptive learning rates, which use increments for the update of the weights which are independent from the absolute partial derivatives. This makes sense, because large flat regions in the search space (plateaus) lead to small absolute partial derivatives and so the increments are chosen small, but the increments should be large to skip the plateau. In contrast, the absolute partial derivatives are very large at the "slopes" of very "narrow canyons", which leads to large increments that will skip the minimum lying at the bottom of the canyon, but it would make more sense to chose small increments to hit the minimum.

So, the Rprop algorithm only uses the signs of the partial derivatives and not the absolute values to adapt the parameters.
Instead of individual learning rates, it uses the parameter \(\Delta_i^{(t)}\) for weight \(w_i,\ i = 1, \dots, n\) in iteration \(t\), where the parameter will be adapted before the change of the weights:

\( \Delta_i^{(t)} = \Bigg\{ \begin{array}{ll} min( \eta^+ \cdot \Delta_i^{(t-1)}, \Delta_{max} ), & \mbox{if\ } \frac{\partial E^{(t-1)}}{\partial w_i} \cdot \frac{\partial E^{(t)}}{\partial w_i} > 0 \\ max( \eta^- \cdot \Delta_i^{(t-1)}, \Delta_{min} ), & \mbox{if\ } \frac{\partial E^{(t-1)}}{\partial w_i} \cdot \frac{\partial E^{(t)}}{\partial w_i} < 0 \\ \Delta_i^{(t-1)}, & \mbox{otherwise} \end{array} \)

The parameters \(\eta^+ > 1\) and \(0 < \eta^- < 1\) control the speed of the adaptation. To stabilize the increments, they are restricted to the interval \([\Delta_{min}, \Delta_{max}]\).
After the adaptation of the \(\Delta_i\) the update for the weights will be calculated as

\( \Delta w_i^{(t)} := - \mbox{sign} \left( \frac{\partial E^{(t)}}{\partial w_i}\right) \cdot \Delta_i^{(t)} \)

There are several variants of the algorithm depending on what happens when the optimum is overstepped, i.e. a sign change of the gradient occurs and/or the new objective value is larger than the old.

Weight-backtracking can be used to increase the stability of the method. if \(\frac{\partial E^{(t-1)}}{\partial w_i} \cdot \frac{\partial E^{(t)}}{\partial w_i} < 0\) then \(\Delta w_i^{(t)} := - \Delta w_i^{(t-1)}\). This heuristic can be improved by further taking the value of the last iteration into ccount: only undo an updated if the sign changed and the new function value is worse than the last. The idea of this modification is, that a change of the sign of the partial derivation \(\frac{\partial E}{\partial w_i}\) only states, that a minimum was skipped and not, whether this step lead to an approach to the minimum or not.

Furthermore, it has been shown to be beneficial to use gradient freezing when the rgadient changes sign, i.e. , if \(\frac{\partial E^{(t-1)}}{\partial w_i} \cdot \frac{\partial E^{(t)}}{\partial w_i} < 0\) then \(\frac{\partial E^{(t)}}{\partial w_i} := 0\); Thus, after an unsuccessful step is performed, delta is not changed for one iteration.

Based on this, 4 major algorithms can be derived: Rprop-: (no backtracking, no freezing) IRprop-: (no backtracking, freezing) Rprop+: (gradient based backtracking, freezing) IRprop+: (function value based backtracking, freezing)

By default, IRprop+ is chosen.

For further information about the algorithm, please refer to:

Martin Riedmiller and Heinrich Braun,
"A Direct Adaptive Method for Faster Backpropagation Learning: The RPROP Algorithm".
In "Proceedings of the IEEE International Conference on Neural Networks", pp. 586-591,
Published by IEEE Press in 1993

Martin Riedmiller,
"Advanced Supervised Learning in Multi-layer Perceptrons - From Backpropagation to Adaptive Learning Algorithms".
In "International Journal of Computer Standards and Interfaces", volume 16, no. 5, 1994, pp. 265-278

Christian Igel and Michael Hüsken,
"Empirical Evaluation of the Improved Rprop Learning Algorithm".
In Neurocomputing Journal, 2002, in press

Definition at line 138 of file Rprop.h.

Member Typedef Documentation

◆ ObjectiveFunctionType

template<class SearchPointType = RealVector>

typedef AbstractObjectiveFunction<SearchPointType,double> shark::Rprop< SearchPointType >::ObjectiveFunctionType

Definition at line 141 of file Rprop.h.

Constructor & Destructor Documentation

◆ Rprop()

template<class SearchPointType = RealVector>

shark::Rprop< SearchPointType >::Rprop ( )

Member Function Documentation

◆ derivative()

template<class SearchPointType = RealVector>

SearchPointType const & shark::Rprop< SearchPointType >::derivative ( ) const

inline

Returns the derivative at the current point. Can be used for stopping criteria.

Definition at line 202 of file Rprop.h.

References shark::Rprop< SearchPointType >::m_derivative.

◆ init() [1/2]

template<class SearchPointType = RealVector>

void shark::Rprop< SearchPointType >::init	(	ObjectiveFunctionType const &	objectiveFunction,
		SearchPointType const &	startingPoint
	)

Referenced by main(), main(), run_one_trial(), and trainProblem().

◆ init() [2/2]

template<class SearchPointType = RealVector>

void shark::Rprop< SearchPointType >::init	(	ObjectiveFunctionType const &	objectiveFunction,
		SearchPointType const &	startingPoint,
		double	initDelta
	)

◆ maxDelta()

template<class SearchPointType = RealVector>

double shark::Rprop< SearchPointType >::maxDelta ( ) const

inline

return the maximal step size component

Definition at line 197 of file Rprop.h.

References shark::Rprop< SearchPointType >::m_delta.

Referenced by run_one_trial().

◆ name()

template<class SearchPointType = RealVector>

std::string shark::Rprop< SearchPointType >::name ( ) const

inlinevirtual

From INameable: return the class name.

Reimplemented from shark::INameable.

Definition at line 145 of file Rprop.h.

◆ read()

template<class SearchPointType = RealVector>

virtual void shark::Rprop< SearchPointType >::read ( InArchive & archive )

virtual

Read the component from the supplied archive.

Parameters

[in,out] archive The archive to read from.

Reimplemented from shark::ISerializable.

◆ setEtaMinus()

template<class SearchPointType = RealVector>

void shark::Rprop< SearchPointType >::setEtaMinus ( double etaMinus )

inline

set decrease factor

Definition at line 158 of file Rprop.h.

References shark::Rprop< SearchPointType >::m_decreaseFactor, and RANGE_CHECK.

◆ setEtaPlus()

template<class SearchPointType = RealVector>

void shark::Rprop< SearchPointType >::setEtaPlus ( double etaPlus )

inline

set increase factor

Definition at line 165 of file Rprop.h.

References shark::Rprop< SearchPointType >::m_increaseFactor, and RANGE_CHECK.

◆ setMaxDelta()

template<class SearchPointType = RealVector>

void shark::Rprop< SearchPointType >::setMaxDelta ( double d )

inline

set upper limit on update

Definition at line 171 of file Rprop.h.

References shark::Rprop< SearchPointType >::m_maxDelta, and RANGE_CHECK.

◆ setMinDelta()

template<class SearchPointType = RealVector>

void shark::Rprop< SearchPointType >::setMinDelta ( double d )

inline

set lower limit on update

Definition at line 177 of file Rprop.h.

References shark::Rprop< SearchPointType >::m_minDelta, and RANGE_CHECK.

◆ setUseBacktracking()

template<class SearchPointType = RealVector>

void shark::Rprop< SearchPointType >::setUseBacktracking ( bool useBacktracking )

inline

Definition at line 192 of file Rprop.h.

References shark::Rprop< SearchPointType >::m_useBacktracking.

◆ setUseFreezing()

template<class SearchPointType = RealVector>

void shark::Rprop< SearchPointType >::setUseFreezing ( bool useFreezing )

inline

Definition at line 189 of file Rprop.h.

References shark::Rprop< SearchPointType >::m_useFreezing.

◆ setUseOldValue()

template<class SearchPointType = RealVector>

void shark::Rprop< SearchPointType >::setUseOldValue ( bool useOldValue )

inline

Definition at line 182 of file Rprop.h.

References shark::AbstractOptimizer< PointType, double, SingleObjectiveResultSet< PointType > >::m_features, shark::Rprop< SearchPointType >::m_useOldValue, shark::AbstractOptimizer< PointType, double, SingleObjectiveResultSet< PointType > >::REQUIRES_VALUE, and shark::TypedFlags< Flag >::reset().

◆ step()

template<class SearchPointType = RealVector>

void shark::Rprop< SearchPointType >::step ( ObjectiveFunctionType const & objectiveFunction )

Referenced by main(), main(), run_one_trial(), and trainProblem().

◆ write()

template<class SearchPointType = RealVector>

virtual void shark::Rprop< SearchPointType >::write ( OutArchive & archive ) const

virtual

Write the component to the supplied archive.

Parameters

[in,out] archive The archive to write to.

Reimplemented from shark::ISerializable.

Member Data Documentation

◆ m_decreaseFactor

template<class SearchPointType = RealVector>

double shark::Rprop< SearchPointType >::m_decreaseFactor

protected

The decrease factor \( \eta^- \), set to 0.5 by default.

Definition at line 212 of file Rprop.h.

Referenced by shark::Rprop< SearchPointType >::setEtaMinus().

◆ m_delta

template<class SearchPointType = RealVector>

SearchPointType shark::Rprop< SearchPointType >::m_delta

protected

The absolute update values (increment) for all weights.

Definition at line 230 of file Rprop.h.

Referenced by shark::Rprop< SearchPointType >::maxDelta().

◆ m_deltaw

template<class SearchPointType = RealVector>

SearchPointType shark::Rprop< SearchPointType >::m_deltaw

protected

the step eprformed last. used for weight backtracking

Definition at line 227 of file Rprop.h.

◆ m_derivative

template<class SearchPointType = RealVector>

SearchPointType shark::Rprop< SearchPointType >::m_derivative

protected

Definition at line 206 of file Rprop.h.

Referenced by shark::Rprop< SearchPointType >::derivative().

◆ m_increaseFactor

template<class SearchPointType = RealVector>

double shark::Rprop< SearchPointType >::m_increaseFactor

protected

The increase factor \( \eta^+ \), set to 1.2 by default.

Definition at line 209 of file Rprop.h.

Referenced by shark::Rprop< SearchPointType >::setEtaPlus().

◆ m_maxDelta

template<class SearchPointType = RealVector>

double shark::Rprop< SearchPointType >::m_maxDelta

protected

The upper limit of the increments \( \Delta w_i^{(t)} \), set to 1e100 by default.

Definition at line 215 of file Rprop.h.

Referenced by shark::Rprop< SearchPointType >::setMaxDelta().

◆ m_minDelta

template<class SearchPointType = RealVector>

double shark::Rprop< SearchPointType >::m_minDelta

protected

The lower limit of the increments \( \Delta w_i^{(t)} \), set to 0.0 by default.

Definition at line 218 of file Rprop.h.

Referenced by shark::Rprop< SearchPointType >::setMinDelta().

◆ m_oldDerivative

template<class SearchPointType = RealVector>

SearchPointType shark::Rprop< SearchPointType >::m_oldDerivative

protected

The last error gradient.

Definition at line 225 of file Rprop.h.

◆ m_oldValue

template<class SearchPointType = RealVector>

double shark::Rprop< SearchPointType >::m_oldValue

protected

The last function value observed.

Definition at line 220 of file Rprop.h.

◆ m_parameterSize

template<class SearchPointType = RealVector>

size_t shark::Rprop< SearchPointType >::m_parameterSize

protected

Definition at line 222 of file Rprop.h.

◆ m_useBacktracking

template<class SearchPointType = RealVector>

bool shark::Rprop< SearchPointType >::m_useBacktracking

protected

Definition at line 233 of file Rprop.h.

Referenced by shark::Rprop< SearchPointType >::setUseBacktracking().

◆ m_useFreezing

template<class SearchPointType = RealVector>

bool shark::Rprop< SearchPointType >::m_useFreezing

protected

Definition at line 232 of file Rprop.h.

Referenced by shark::Rprop< SearchPointType >::setUseFreezing().

◆ m_useOldValue

template<class SearchPointType = RealVector>

bool shark::Rprop< SearchPointType >::m_useOldValue

protected

Definition at line 234 of file Rprop.h.

Referenced by shark::Rprop< SearchPointType >::setUseOldValue().

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

include/shark/Algorithms/GradientDescent/Rprop.h

Public Types

Public Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

Member Typedef Documentation

◆ ObjectiveFunctionType

Constructor & Destructor Documentation

◆ Rprop()

Member Function Documentation

◆ derivative()

◆ init() [1/2]

◆ init() [2/2]

◆ maxDelta()

◆ name()

◆ read()

◆ setEtaMinus()

◆ setEtaPlus()

◆ setMaxDelta()

◆ setMinDelta()

◆ setUseBacktracking()

◆ setUseFreezing()

◆ setUseOldValue()

◆ step()

◆ write()

Member Data Documentation

◆ m_decreaseFactor

◆ m_delta

◆ m_deltaw

◆ m_derivative

◆ m_increaseFactor

◆ m_maxDelta

◆ m_minDelta

◆ m_oldDerivative

◆ m_oldValue

◆ m_parameterSize

◆ m_useBacktracking

◆ m_useFreezing

◆ m_useOldValue