Stochastic Gradient Descent is a technique for minimizing a function which can be expressed as a sum of other functions. More...

Inheritance diagram for SGD< UpdatePolicyType, DecayPolicyType >:

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Public Member Functions
	SGD (const double stepSize=0.01, const size_t batchSize=32, const size_t maxIterations=100000, const double tolerance=1e-5, const bool shuffle=true, const UpdatePolicyType &updatePolicy=UpdatePolicyType(), const DecayPolicyType &decayPolicy=DecayPolicyType(), const bool resetPolicy=true)
	Construct the SGD 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...

const DecayPolicyType &	DecayPolicy () const
	Get the step size decay policy. More...

DecayPolicyType &	DecayPolicy ()
	Modify the step size decay policy. 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 stochastic gradient descent. More...

bool	ResetPolicy () const
	Get whether or not the update policy parameters are reset before Optimize call. More...

bool &	ResetPolicy ()
	Modify whether or not the update policy parameters are reset before Optimize call. 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
=
VanillaUpdate
,
typename
DecayPolicyType
=
NoDecay
>

class mlpack::optimization::SGD< UpdatePolicyType, DecayPolicyType >

Stochastic Gradient Descent is a technique for minimizing a function which can be expressed as a sum of other functions.

That is, suppose we have

$f(A) = \sum_{i = 0}^{n} f_i(A)$

and our task is to minimize $ A $ . Stochastic gradient descent iterates over each function $ f_i(A) $ , based on the specified update policy. By default vanilla update policy (see mlpack::optimization::VanillaUpdate) is used. The SGD class supports either scanning through each of the $ n $ functions $ f_i(A)$ linearly, or in a random sequence. The algorithm continues until $ j$ reaches the maximum number of iterations—or when a full sequence of updates through each of the $ n $ functions $ f_i(A) $ produces an improvement within a certain tolerance $\epsilon$ . That is,

$| f(A_{j + n}) - f(A_j) | < \epsilon.$

The parameter $\epsilon$ is specified by the tolerance parameter to the constructor; $n$ is specified by the maxIterations parameter.

This class is useful for data-dependent functions whose objective function can be expressed as a sum of objective functions operating on an individual point. Then, SGD considers the gradient of the objective function operating on an individual point in its update of $ A $ .

For SGD 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 ( $n$ ), 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

UpdatePolicyType	update policy used by SGD during the iterative update process. By default vanilla update policy (see mlpack::optimization::VanillaUpdate) is used.
DecayPolicyType	Decay policy used during the iterative update process to adjust the step size. By default the step size isn't going to be adjusted (i.e. NoDecay is used).

Definition at line 86 of file sgd.hpp.

Constructor & Destructor Documentation

◆ SGD()

SGD	(	const double	stepSize = `0.01`,
		const size_t	batchSize = `32`,
		const size_t	maxIterations = `100000`,
		const double	tolerance = `1e-5`,
		const bool	shuffle = `true`,
		const UpdatePolicyType &	updatePolicy = `UpdatePolicyType()`,
		const DecayPolicyType &	decayPolicy = `DecayPolicyType()`,
		const bool	resetPolicy = `true`
	)

Construct the SGD 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).
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.
decayPolicy	Instantiated decay policy used to adjust the step size.
resetPolicy	Flag that determines whether update policy parameters are reset before every Optimize call.

Member Function Documentation

◆ BatchSize() [1/2]

size_t BatchSize ( ) const

inline

Get the batch size.

Definition at line 139 of file sgd.hpp.

Referenced by SGDR< UpdatePolicyType >::BatchSize(), SnapshotSGDR< UpdatePolicyType >::BatchSize(), and AdamType< UpdateRule >::BatchSize().

◆ BatchSize() [2/2]

size_t& BatchSize ( )

inline

Modify the batch size.

Definition at line 141 of file sgd.hpp.

◆ DecayPolicy() [1/2]

const DecayPolicyType& DecayPolicy ( ) const

inline

Get the step size decay policy.

Definition at line 171 of file sgd.hpp.

Referenced by SnapshotSGDR< UpdatePolicyType >::Snapshots().

◆ DecayPolicy() [2/2]

DecayPolicyType& DecayPolicy ( )

inline

Modify the step size decay policy.

Definition at line 173 of file sgd.hpp.

◆ MaxIterations() [1/2]

size_t MaxIterations ( ) const

inline

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

Definition at line 144 of file sgd.hpp.

Referenced by SGDR< UpdatePolicyType >::MaxIterations(), SnapshotSGDR< UpdatePolicyType >::MaxIterations(), and AdamType< UpdateRule >::MaxIterations().

◆ MaxIterations() [2/2]

size_t& MaxIterations ( )

inline

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

Definition at line 146 of file sgd.hpp.

◆ Optimize()

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

Optimize the given function using stochastic gradient descent.

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.

Referenced by AdamType< UpdateRule >::Optimize().

◆ ResetPolicy() [1/2]

bool ResetPolicy ( ) const

inline

Get whether or not the update policy parameters are reset before Optimize call.

Definition at line 160 of file sgd.hpp.

◆ ResetPolicy() [2/2]

bool& ResetPolicy ( )

inline

Modify whether or not the update policy parameters are reset before Optimize call.

Definition at line 163 of file sgd.hpp.

◆ Shuffle() [1/2]

bool Shuffle ( ) const

inline

Get whether or not the individual functions are shuffled.

Definition at line 154 of file sgd.hpp.

Referenced by SGDR< UpdatePolicyType >::Shuffle(), SnapshotSGDR< UpdatePolicyType >::Shuffle(), and AdamType< UpdateRule >::Shuffle().

◆ Shuffle() [2/2]

bool& Shuffle ( )

inline

Modify whether or not the individual functions are shuffled.

Definition at line 156 of file sgd.hpp.

◆ StepSize() [1/2]

double StepSize ( ) const

inline

Get the step size.

Definition at line 134 of file sgd.hpp.

Referenced by SGDR< UpdatePolicyType >::StepSize(), SnapshotSGDR< UpdatePolicyType >::StepSize(), and AdamType< UpdateRule >::StepSize().

◆ StepSize() [2/2]

double& StepSize ( )

inline

Modify the step size.

Definition at line 136 of file sgd.hpp.

◆ Tolerance() [1/2]

double Tolerance ( ) const

inline

Get the tolerance for termination.

Definition at line 149 of file sgd.hpp.

Referenced by SGDR< UpdatePolicyType >::Tolerance(), SnapshotSGDR< UpdatePolicyType >::Tolerance(), and AdamType< UpdateRule >::Tolerance().

◆ Tolerance() [2/2]

double& Tolerance ( )

inline

Modify the tolerance for termination.

Definition at line 151 of file sgd.hpp.

◆ UpdatePolicy() [1/2]

const UpdatePolicyType& UpdatePolicy ( ) const

inline

Get the update policy.

Definition at line 166 of file sgd.hpp.

Referenced by AdamType< UpdateRule >::Beta1(), AdamType< UpdateRule >::Beta2(), AdamType< UpdateRule >::Epsilon(), SGDR< UpdatePolicyType >::UpdatePolicy(), and SnapshotSGDR< UpdatePolicyType >::UpdatePolicy().

◆ UpdatePolicy() [2/2]

UpdatePolicyType& UpdatePolicy ( )

inline

Modify the update policy.

Definition at line 168 of file sgd.hpp.

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

src/mlpack/core/optimizers/sgd/sgd.hpp

Public Member Functions

Detailed Description

template<typenameUpdatePolicyType=VanillaUpdate,typenameDecayPolicyType=NoDecay> class mlpack::optimization::SGD< UpdatePolicyType, DecayPolicyType >

Constructor & Destructor Documentation

◆ SGD()

Member Function Documentation

◆ BatchSize() [1/2]

◆ BatchSize() [2/2]

◆ DecayPolicy() [1/2]

◆ DecayPolicy() [2/2]

◆ MaxIterations() [1/2]

◆ MaxIterations() [2/2]

◆ Optimize()

◆ ResetPolicy() [1/2]

◆ ResetPolicy() [2/2]

◆ Shuffle() [1/2]

◆ Shuffle() [2/2]

◆ StepSize() [1/2]

◆ StepSize() [2/2]

◆ Tolerance() [1/2]

◆ Tolerance() [2/2]

◆ UpdatePolicy() [1/2]

◆ UpdatePolicy() [2/2]

template
<
typename
UpdatePolicyType
=
VanillaUpdate
,
typename
DecayPolicyType
=
NoDecay
>

class mlpack::optimization::SGD< UpdatePolicyType, DecayPolicyType >