Adam is an optimizer that computes individual adaptive learning rates for different parameters from estimates of first and second moments of the gradients. More...

Public Member Functions
	AdamType (const double stepSize=0.001, const size_t batchSize=32, const double beta1=0.9, const double beta2=0.999, const double eps=1e-8, const size_t maxIterations=100000, const double tolerance=1e-5, const bool shuffle=true)
	Construct the Adam 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...

double	Beta1 () const
	Get the smoothing parameter. More...

double &	Beta1 ()
	Modify the smoothing parameter. More...

double	Beta2 () const
	Get the second moment coefficient. More...

double &	Beta2 ()
	Modify the second moment coefficient. 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...

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 Adam. 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...

Detailed Description

template
<
typename
UpdateRule
=
AdamUpdate
>

class mlpack::optimization::AdamType< UpdateRule >

Adam is an optimizer that computes individual adaptive learning rates for different parameters from estimates of first and second moments of the gradients.

AdaMax is a variant of Adam based on the infinity norm as given in the section 7 of the following paper. Nadam is an optimizer that combines the Adam and NAG. NadaMax is an variant of Nadam based on Infinity form.

For more information, see the following.

@article{Kingma2014,
  author  = {Diederik P. Kingma and Jimmy Ba},
  title   = {Adam: {A} Method for Stochastic Optimization},
  journal = {CoRR},
  year    = {2014},
  url     = {http://arxiv.org/abs/1412.6980}
}
@article{
  title   = {On the convergence of Adam and beyond},
  url     = {https://openreview.net/pdf?id=ryQu7f-RZ}
  year    = {2018}
}

For Adam, AdaMax, AMSGrad, Nadam and NadaMax 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

UpdateRule Adam optimizer update rule to be used.

Definition at line 87 of file adam.hpp.

Constructor & Destructor Documentation

◆ AdamType()

AdamType	(	const double	stepSize = `0.001`,
		const size_t	batchSize = `32`,
		const double	beta1 = `0.9`,
		const double	beta2 = `0.999`,
		const double	eps = `1e-8`,
		const size_t	maxIterations = `100000`,
		const double	tolerance = `1e-5`,
		const bool	shuffle = `true`
	)

Construct the Adam 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	Number of points to process in a single step.
beta1	Exponential decay rate for the first moment estimates.
beta2	Exponential decay rate for the weighted infinity norm estimates.
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

◆ BatchSize() [1/2]

size_t BatchSize ( ) const

inline

Get the batch size.

Definition at line 141 of file adam.hpp.

References SGD< UpdatePolicyType, DecayPolicyType >::BatchSize().

◆ BatchSize() [2/2]

size_t& BatchSize ( )

inline

Modify the batch size.

Definition at line 143 of file adam.hpp.

References SGD< UpdatePolicyType, DecayPolicyType >::BatchSize().

◆ Beta1() [1/2]

double Beta1 ( ) const

inline

Get the smoothing parameter.

Definition at line 146 of file adam.hpp.

References SGD< UpdatePolicyType, DecayPolicyType >::UpdatePolicy().

◆ Beta1() [2/2]

double& Beta1 ( )

inline

Modify the smoothing parameter.

Definition at line 148 of file adam.hpp.

References SGD< UpdatePolicyType, DecayPolicyType >::UpdatePolicy().

◆ Beta2() [1/2]

double Beta2 ( ) const

inline

Get the second moment coefficient.

Definition at line 151 of file adam.hpp.

References SGD< UpdatePolicyType, DecayPolicyType >::UpdatePolicy().

◆ Beta2() [2/2]

double& Beta2 ( )

inline

Modify the second moment coefficient.

Definition at line 153 of file adam.hpp.

References SGD< UpdatePolicyType, DecayPolicyType >::UpdatePolicy().

◆ Epsilon() [1/2]

double Epsilon ( ) const

inline

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

Definition at line 156 of file adam.hpp.

References SGD< UpdatePolicyType, DecayPolicyType >::UpdatePolicy().

◆ Epsilon() [2/2]

double& Epsilon ( )

inline

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

Definition at line 158 of file adam.hpp.

References SGD< UpdatePolicyType, DecayPolicyType >::UpdatePolicy().

◆ MaxIterations() [1/2]

size_t MaxIterations ( ) const

inline

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

Definition at line 161 of file adam.hpp.

References SGD< UpdatePolicyType, DecayPolicyType >::MaxIterations().

◆ MaxIterations() [2/2]

size_t& MaxIterations ( )

inline

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

Definition at line 163 of file adam.hpp.

References SGD< UpdatePolicyType, DecayPolicyType >::MaxIterations().

◆ Optimize()

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

inline

Optimize the given function using Adam.

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 optimize.

Parameters

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

Returns: Objective value of the final point.

Definition at line 130 of file adam.hpp.

References SGD< UpdatePolicyType, DecayPolicyType >::Optimize().

◆ Shuffle() [1/2]

bool Shuffle ( ) const

inline

Get whether or not the individual functions are shuffled.

Definition at line 171 of file adam.hpp.

References SGD< UpdatePolicyType, DecayPolicyType >::Shuffle().

◆ Shuffle() [2/2]

bool& Shuffle ( )

inline

Modify whether or not the individual functions are shuffled.

Definition at line 173 of file adam.hpp.

References SGD< UpdatePolicyType, DecayPolicyType >::Shuffle().

◆ StepSize() [1/2]

double StepSize ( ) const

inline

Get the step size.

Definition at line 136 of file adam.hpp.

References SGD< UpdatePolicyType, DecayPolicyType >::StepSize().

◆ StepSize() [2/2]

double& StepSize ( )

inline

Modify the step size.

Definition at line 138 of file adam.hpp.

References SGD< UpdatePolicyType, DecayPolicyType >::StepSize().

◆ Tolerance() [1/2]

double Tolerance ( ) const

inline

Get the tolerance for termination.

Definition at line 166 of file adam.hpp.

References SGD< UpdatePolicyType, DecayPolicyType >::Tolerance().

◆ Tolerance() [2/2]

double& Tolerance ( )

inline

Modify the tolerance for termination.

Definition at line 168 of file adam.hpp.

References SGD< UpdatePolicyType, DecayPolicyType >::Tolerance().

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

src/mlpack/core/optimizers/adam/adam.hpp

Public Member Functions

Detailed Description

template<typenameUpdateRule=AdamUpdate> class mlpack::optimization::AdamType< UpdateRule >

Constructor & Destructor Documentation

◆ AdamType()

Member Function Documentation

◆ BatchSize() [1/2]

◆ BatchSize() [2/2]

◆ Beta1() [1/2]

◆ Beta1() [2/2]

◆ Beta2() [1/2]

◆ Beta2() [2/2]

◆ Epsilon() [1/2]

◆ Epsilon() [2/2]

◆ MaxIterations() [1/2]

◆ MaxIterations() [2/2]

◆ Optimize()

◆ Shuffle() [1/2]

◆ Shuffle() [2/2]

◆ StepSize() [1/2]

◆ StepSize() [2/2]

◆ Tolerance() [1/2]

◆ Tolerance() [2/2]

template
<
typename
UpdateRule
=
AdamUpdate
>

class mlpack::optimization::AdamType< UpdateRule >