Limited-Memory Broyden, Fletcher, Goldfarb, Shannon algorithm. More...

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

Inheritance diagram for shark::LBFGS:

Public Member Functions
	LBFGS ()

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

void	setHistCount (unsigned int numhist)
	Specify the amount of steps to be memorized and used to find the L-BFGS direction. More...

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

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

Public Member Functions inherited from shark::AbstractLineSearchOptimizer
SHARK_EXPORT_SYMBOL	AbstractLineSearchOptimizer ()

SHARK_EXPORT_SYMBOL void	init (ObjectiveFunctionType const &objectiveFunction, SearchPointType const &startingPoint)
	initializes the optimizer using a predefined starting point More...

SHARK_EXPORT_SYMBOL void	step (ObjectiveFunctionType const &objectiveFunction)
	Carry out one step of the optimizer for the supplied objective function. More...

LineSearch const &	lineSearch () const

LineSearch &	lineSearch ()

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

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

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. More...

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

Public Member Functions inherited from shark::AbstractOptimizer< RealVector, double, SingleObjectiveResultSet< RealVector > >
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. More...

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

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

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

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

	BOOST_SERIALIZATION_SPLIT_MEMBER ()

Protected Member Functions
SHARK_EXPORT_SYMBOL void	initModel ()
	Initializes the internal model. More...

SHARK_EXPORT_SYMBOL void	computeSearchDirection (ObjectiveFunctionType const &)
	Updates the Model and computes the next search direction. More...

Protected Member Functions inherited from shark::AbstractOptimizer< RealVector, double, SingleObjectiveResultSet< RealVector > >
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. More...

Additional Inherited Members
Public Types inherited from shark::AbstractSingleObjectiveOptimizer< RealVector >
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< RealVector, double, SingleObjectiveResultSet< RealVector > >
enum	Feature
	Models features that the optimizer requires from the objective function. More...

typedef RealVector	SearchPointType

typedef double	ResultType

typedef SingleObjectiveResultSet< RealVector >	SolutionType

typedef AbstractObjectiveFunction< RealVector, ResultType >	ObjectiveFunctionType

typedef TypedFlags< Feature >	Features

typedef TypedFeatureNotAvailableException< Feature >	FeatureNotAvailableException

Protected Attributes inherited from shark::AbstractLineSearchOptimizer
LineSearch	m_linesearch
	used line search method. More...

std::size_t	m_dimension
	number of parameters More...

double	m_initialStepLength
	Initial step length to begin with the line search. More...

RealVector	m_derivative
	gradient of m_best.point More...

RealVector	m_searchDirection
	search direction of next step More...

RealVector	m_lastPoint
	previous point More...

RealVector	m_lastDerivative
	gradient of the previous point More...

double	m_lastValue
	value of the previous point More...

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

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

Detailed Description

Limited-Memory Broyden, Fletcher, Goldfarb, Shannon algorithm.

BFGS is one of the best performing quasi-newton methods. However for large scale optimization, storing the full hessian approximation is infeasible due to O(n^2) memory requirement. The L-BFGS algorithm does not store the full hessian approximation but only stores the data used for updating in the last steps. The matrix itself is then regenerated on-the-fly in an implicit matrix scheme. This brings runtime and memory rquirements of a single step down to O(n*hist_size).

The number of steps stored can be set with setHistCount. This is 100 as default.

The algorithm is implemented for unconstrained and constrained optimization in the case of box constraints. When box constraints are present and the algorithm encounters a constraint, a dog-leg style algorithm is used:

first, all variables with active constraints (e.g. x_i = l_i and g_i > 0) are fixed, i.e. p_i = 0. For the remaining variables, the unconstrained optimization problem is solved. If the solution does not statisfy the box constraints, in the next step the cauchy point is computed. If the cauchy point is feasible, we search the point along the line between unconstrained optimum and cauchy point that lies exactly on the constraint. This is the point with smallest value along the path. This does not find the true optimal step in the unconstrained problem, however a cheap and reasonably good optimum which often improves over naive coordinate descent.

Definition at line 72 of file LBFGS.h.

Constructor & Destructor Documentation

◆ LBFGS()

shark::LBFGS::LBFGS ( )

inline

Definition at line 74 of file LBFGS.h.

References shark::AbstractOptimizer< RealVector, double, SingleObjectiveResultSet< RealVector > >::CAN_SOLVE_CONSTRAINED, and shark::AbstractOptimizer< RealVector, double, SingleObjectiveResultSet< RealVector > >::m_features.

Member Function Documentation

◆ computeSearchDirection()

SHARK_EXPORT_SYMBOL void shark::LBFGS::computeSearchDirection ( ObjectiveFunctionType const & objectiveFunction )

protectedvirtual

Updates the Model and computes the next search direction.

After a step was performed, this method is called to compute the next search direction. This usually involves updating the internal model using the new and old step information. Afterwards m_searchDirection should contain the next search direction.

Implements shark::AbstractLineSearchOptimizer.

Referenced by setHistCount().

◆ initModel()

SHARK_EXPORT_SYMBOL void shark::LBFGS::initModel ( )

protectedvirtual

Initializes the internal model.

Line Search Methods use a Model to search for the next search direction. The model is initialized during init()

Implements shark::AbstractLineSearchOptimizer.

Referenced by setHistCount().

◆ name()

std::string shark::LBFGS::name ( ) const

inlinevirtual

From INameable: return the class name.

Reimplemented from shark::INameable.

Definition at line 79 of file LBFGS.h.

◆ read()

SHARK_EXPORT_SYMBOL void shark::LBFGS::read ( InArchive & archive )

virtual

Read the component from the supplied archive.

Parameters

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

Reimplemented from shark::AbstractLineSearchOptimizer.

Referenced by setHistCount().

◆ setHistCount()

void shark::LBFGS::setHistCount ( unsigned int numhist )

inline

Specify the amount of steps to be memorized and used to find the L-BFGS direction.

Parameters

numhist The amount of steps to use.

Definition at line 85 of file LBFGS.h.

References computeSearchDirection(), initModel(), read(), SHARK_EXPORT_SYMBOL, SHARK_RUNTIME_CHECK, shark::AbstractLineSearchOptimizer::step(), and write().

◆ write()

SHARK_EXPORT_SYMBOL void shark::LBFGS::write ( OutArchive & archive ) const

virtual

Write the component to the supplied archive.

Parameters

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

Reimplemented from shark::AbstractLineSearchOptimizer.

Referenced by setHistCount().

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

include/shark/Algorithms/GradientDescent/LBFGS.h

Public Member Functions

Protected Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ LBFGS()

Member Function Documentation

◆ computeSearchDirection()

◆ initModel()

◆ name()

◆ read()

◆ setHistCount()

◆ write()