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BigBatchSGD< UpdatePolicyType > Class Template Reference

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

Public Member Functions

 BigBatchSGD (const size_t batchSize=1000, const double stepSize=0.01, const double batchDelta=0.1, const size_t maxIterations=100000, const double tolerance=1e-5, const bool shuffle=true)
 Construct the BigBatchSGD optimizer with the given function and parameters. More...

 
double BatchDelta () const
 Get the batch delta. More...

 
double & BatchDelta ()
 Modify the batch delta. More...

 
size_t BatchSize () const
 Get the batch size. More...

 
size_t & BatchSize ()
 Modify the batch size. 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 big-batch SGD. 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...

 
UpdatePolicyType UpdatePolicy () const
 Get the update policy. More...

 
UpdatePolicyType & UpdatePolicy ()
 Modify the update policy. More...

 

Detailed Description


template
<
typename
UpdatePolicyType
=
AdaptiveStepsize
>

class mlpack::optimization::BigBatchSGD< UpdatePolicyType >

Big-batch 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 $. Big-batch SGD iterates over batches of functions $ \{ f_{i0}(A), f_{i1}(A), \ldots, f_{i(m - 1)}(A) $ for some batch size $ m $, producing the following update scheme:

\[ A_{j + 1} = A_j + \alpha \left(\sum_{k = 0}^{m - 1} \nabla f_{ik}(A) \right) \]

where $ \alpha $ is a parameter which specifies the step size. Each big-batch is passed through either sequentially or randomly. The algorithm continues until $ j $ reaches the maximum number of iterations—or when a full sequence of updates through each of the big-batches produces an improvement within a certain tolerance $ \epsilon $.

The parameter $ \epsilon $ is specified by the tolerance parameter tot he constructor, as is the maximum number of iterations 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, big-batch SGD considers the gradient of the objective function operation on an individual big-batch of points in its update of $ A $.

For more information, please refer to:

@article{De2017,
title = {Big Batch {SGD:} Automated Inference using Adaptive Batch
Sizes},
author = {Soham De and Abhay Kumar Yadav and David W. Jacobs and
Tom Goldstein},
journal = {CoRR},
year = {2017},
url = {http://arxiv.org/abs/1610.05792},
}

For big-batch 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); void Gradient(const arma::mat& coordinates, const size_t i, arma::mat& gradient);

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 (presumably, the dataset is held internally in the DecomposableFunctionType).

Template Parameters
UpdatePolicyTypeUpdate policy used during the iterative update process. By default the AdaptiveStepsize update policy is used.

Definition at line 93 of file bigbatch_sgd.hpp.

Constructor & Destructor Documentation

◆ BigBatchSGD()

BigBatchSGD ( const size_t  batchSize = 1000,
const double  stepSize = 0.01,
const double  batchDelta = 0.1,
const size_t  maxIterations = 100000,
const double  tolerance = 1e-5,
const bool  shuffle = true 
)

Construct the BigBatchSGD 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 for the task at hand. The maximum number of iterations refers to the maximum number of batches that are processed.

Parameters
batchSizeInitial batch size.
stepSizeStep size for each iteration.
batchDeltaFactor for the batch update step.
maxIterationsMaximum number of iterations allowed (0 means no limit).
toleranceMaximum absolute tolerance to terminate algorithm.
shuffleIf true, the batch order is shuffled; otherwise, each batch is visited in linear order.

Member Function Documentation

◆ BatchDelta() [1/2]

double BatchDelta ( ) const
inline

Get the batch delta.

Definition at line 143 of file bigbatch_sgd.hpp.

◆ BatchDelta() [2/2]

double& BatchDelta ( )
inline

Modify the batch delta.

Definition at line 145 of file bigbatch_sgd.hpp.

◆ BatchSize() [1/2]

size_t BatchSize ( ) const
inline

Get the batch size.

Definition at line 133 of file bigbatch_sgd.hpp.

◆ BatchSize() [2/2]

size_t& BatchSize ( )
inline

Modify the batch size.

Definition at line 135 of file bigbatch_sgd.hpp.

◆ MaxIterations() [1/2]

size_t MaxIterations ( ) const
inline

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

Definition at line 148 of file bigbatch_sgd.hpp.

◆ MaxIterations() [2/2]

size_t& MaxIterations ( )
inline

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

Definition at line 150 of file bigbatch_sgd.hpp.

◆ Optimize()

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

Optimize the given function using big-batch SGD.

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

Template Parameters
DecomposableFunctionTypeType of the function to be optimized.
Parameters
functionFunction to optimize.
iterateStarting 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 158 of file bigbatch_sgd.hpp.

◆ Shuffle() [2/2]

bool& Shuffle ( )
inline

Modify whether or not the individual functions are shuffled.

Definition at line 160 of file bigbatch_sgd.hpp.

◆ StepSize() [1/2]

double StepSize ( ) const
inline

Get the step size.

Definition at line 138 of file bigbatch_sgd.hpp.

◆ StepSize() [2/2]

double& StepSize ( )
inline

Modify the step size.

Definition at line 140 of file bigbatch_sgd.hpp.

◆ Tolerance() [1/2]

double Tolerance ( ) const
inline

Get the tolerance for termination.

Definition at line 153 of file bigbatch_sgd.hpp.

◆ Tolerance() [2/2]

double& Tolerance ( )
inline

Modify the tolerance for termination.

Definition at line 155 of file bigbatch_sgd.hpp.

◆ UpdatePolicy() [1/2]

UpdatePolicyType UpdatePolicy ( ) const
inline

Get the update policy.

Definition at line 163 of file bigbatch_sgd.hpp.

◆ UpdatePolicy() [2/2]

UpdatePolicyType& UpdatePolicy ( )
inline

Modify the update policy.

Definition at line 165 of file bigbatch_sgd.hpp.

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