SARAHType< UpdatePolicyType > Class Template Reference

StochAstic Recusive gRadient algoritHm (SARAH). More...

Public Member Functions
	SARAHType (const double stepSize=0.01, const size_t batchSize=32, const size_t maxIterations=1000, const size_t innerIterations=0, const double tolerance=1e-5, const bool shuffle=true, const UpdatePolicyType &updatePolicy=UpdatePolicyType())
	Construct the SARAH optimizer with the given function and parameters. More...
size_t	BatchSize () const
	Get the batch size. More...
size_t &	BatchSize ()
	Modify the batch size. More...
size_t	InnerIterations () const
	Get the maximum number of iterations (0 indicates default n / b). More...
size_t &	InnerIterations ()
	Modify the maximum number of iterations (0 indicates default n / b). 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...
template < typename DecomposableFunctionType >
double	Optimize (DecomposableFunctionType &function, arma::mat &iterate)
	Optimize the given function using SARAH. 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	StepSize () const
	Get the step size. More...
double &	StepSize ()
	Modify the step size. More...
double	Tolerance () const
	Get the tolerance for termination. More...
double &	Tolerance ()
	Modify the tolerance for termination. More...
const UpdatePolicyType &	UpdatePolicy () const
	Get the update policy. More...
UpdatePolicyType &	UpdatePolicy ()
	Modify the update policy. More...

Detailed Description

template

<

typename

UpdatePolicyType

=

SARAHUpdate

>

class mlpack::optimization::SARAHType< UpdatePolicyType >

StochAstic Recusive gRadient algoritHm (SARAH).

is a variance reducing stochastic recursive gradient algorithm for minimizing a function which can be expressed as a sum of other functions.

For more information, see the following.

@article{Nguyen2017,
  author  = {{Nguyen}, L.~M. and {Liu}, J. and {Scheinberg},
             K. and {Tak{\'a}{\v c}}, M.},
  title   = {SARAH: A Novel Method for Machine Learning Problems Using
             Stochastic Recursive Gradient},
  journal = {ArXiv e-prints},
  url     = {https://arxiv.org/abs/1703.00102}
  year    = 2017,
}

For SARAH 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, const size_t batchSize); void Gradient(const arma::mat& coordinates, const size_t i, arma::mat& gradient, const size_t batchSize);

NumFunctions() should return the number of functions ( ), 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 ( is held internally in the DecomposableFunctionType).

Template Parameters

UpdatePolicyType

update policy used by SARAHType during the iterative update process.

Definition at line 66 of file sarah.hpp.

Constructor & Destructor Documentation

SARAHType()

SARAHType	(	const double	stepSize = 0.01,
		const size_t	batchSize = 32,
		const size_t	maxIterations = 1000,
		const size_t	innerIterations = 0,
		const double	tolerance = 1e-5,
		const bool	shuffle = true,
		const UpdatePolicyType &	updatePolicy = UpdatePolicyType()
	)

Construct the SARAH 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

stepSize	Step size for each iteration.
batchSize	Batch size to use for each step.
maxIterations	Maximum number of iterations allowed (0 means no limit).
innerIterations	The number of inner iterations allowed (0 means n / batchSize). Note that the full gradient is only calculated in the outer iteration.
tolerance	Maximum absolute tolerance to terminate algorithm.
shuffle	If true, the function order is shuffled; otherwise, each function is visited in linear order.
updatePolicy	Instantiated update policy used to adjust the given parameters.

Member Function Documentation

BatchSize() [1/2]

size_t BatchSize ( ) const

inline

Get the batch size.

Definition at line 117 of file sarah.hpp.

BatchSize() [2/2]

size_t& BatchSize ( )

inline

Modify the batch size.

Definition at line 119 of file sarah.hpp.

InnerIterations() [1/2]

size_t InnerIterations ( ) const

inline

Get the maximum number of iterations (0 indicates default n / b).

Definition at line 127 of file sarah.hpp.

InnerIterations() [2/2]

size_t& InnerIterations ( )

inline

Modify the maximum number of iterations (0 indicates default n / b).

Definition at line 129 of file sarah.hpp.

MaxIterations() [1/2]

size_t MaxIterations ( ) const

inline

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

Definition at line 122 of file sarah.hpp.

MaxIterations() [2/2]

size_t& MaxIterations ( )

inline

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

Definition at line 124 of file sarah.hpp.

Optimize()

double Optimize	(	DecomposableFunctionType &	function,
		arma::mat &	iterate
	)

Optimize the given function using SARAH.

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

Template Parameters

DecomposableFunctionType

Type of the function to be optimized.

Parameters

function	Function to optimize.
iterate	Starting point (will be modified).

Returns

Objective value of the final point.

Shuffle() [1/2]

bool Shuffle ( ) const

inline

Get whether or not the individual functions are shuffled.

Definition at line 137 of file sarah.hpp.

Shuffle() [2/2]

bool& Shuffle ( )

inline

Modify whether or not the individual functions are shuffled.

Definition at line 139 of file sarah.hpp.

StepSize() [1/2]

double StepSize ( ) const

inline

Get the step size.

Definition at line 112 of file sarah.hpp.

StepSize() [2/2]

double& StepSize ( )

inline

Modify the step size.

Definition at line 114 of file sarah.hpp.

Tolerance() [1/2]

double Tolerance ( ) const

inline

Get the tolerance for termination.

Definition at line 132 of file sarah.hpp.

Tolerance() [2/2]

double& Tolerance ( )

inline

Modify the tolerance for termination.

Definition at line 134 of file sarah.hpp.

UpdatePolicy() [1/2]

const UpdatePolicyType& UpdatePolicy ( ) const

inline

Get the update policy.

Definition at line 142 of file sarah.hpp.

UpdatePolicy() [2/2]

UpdatePolicyType& UpdatePolicy ( )

inline

Modify the update policy.

Definition at line 144 of file sarah.hpp.

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

• src/mlpack/core/optimizers/sarah/sarah.hpp