Computation
Algorithm Input
OptionalDataID

Input
 

correctionPairs 
Numeric table of size 2
m
x
p
where the rows represent correction pairs
s
and
y
. The row
correctionPairs
[
j
], 0 ≤
j
<
m
, is a correction vector
s _{
j}
, and the row
correctionPairs
[
j
],
m
≤
j
< 2
m
, is a correction vector
y _{
j}
.
 
correctionIndices 
Numeric table of size 1 x 2 with 32bit integer indexes. The first value is the index of correction pair
t
, the second value is the index of last iteration
k
from the previous run.
 
averageArgumentLIterations 
Numeric table of size 2 x
p
, where row 0 represents average arguments for previous
L
iterations, and row 1 represents average arguments for last
L
iterations. These values are required to compute
s
correction vectors in the next step. See step
6.b.iii
of the limitedmemory BFGS algorithm.

Algorithm Parameters
Parameter

Default Value

Description
 

algorithmFPType 
float 
The floatingpoint type that the algorithm uses for intermediate computations. Can be
float
or
double
.
 
method 
defaultDense 
Performanceoriented computation method.
 
batchIndices 
NULL 
The numeric table of size
nIterations
x
batchSize
with 32bit integer indices of terms in the objective function to be used in
step 2
of the limitedmemory BFGS algorithm. If no indices are provided, the implementation generates random indices.
This parameter can be an object of any class derived from
NumericTable
, except for
PackedTriangularMatrix
,
PackedSymmetricMatrix
, and
CSRNumericTable
.
 
batchSize 
10

The number of observations to compute the stochastic gradient. The implementation of the algorithm ignores this parameter if the
batchIndices
numeric table is provided.
If
BatchSize
equals the number of terms in the objective function, no random sampling is performed and all terms are used to calculate the gradient.
 
correctionPairBatchSize 
100

The number of observations to compute the subsampled Hessian for correction pairs computation in step
6.b.ii
of the limitedmemory BFGS algorithm. The implementation of the algorithm ignores this parameter if the
correctionPairIndices
numeric table is provided.
If
correctionPairBatchSize
equals the number of terms in the objective function, no random sampling is performed and all terms are used to calculate the Hessian matrix.
 
correctionPairIndices 
NULL 
The numeric table of size (
nIterations
/
L
) x
correctionPairBatchSize
with 32bit integer indices to be used instead of random values in step
6.b.i
of the limitedmemory BFGS algorithm. If no indices are provided, the implementation generates random indices.
This parameter can be an object of any class derived from
NumericTable
, except for
PackedTriangularMatrix
,
PackedSymmetricMatrix
, and
CSRNumericTable
.
If the algorithm runs with no optional input data, (
nIterations
/
L
 1) rows of the table are used. Otherwise, it can use one more row, (
nIterations
/
L
) in total.
 
m 
10

The memory parameter. The maximum number of correction pairs that define the approximation of the Hessian matrix.
 
L 
10

The number of iterations between calculations of the curvature estimates.
 
stepLengthSequence 
Numeric table of size 1 x 1 that contains the default step length equal to 1.

The numeric table of size 1 x
nIterations
or 1 x 1. The contents of the table depend on its size:
This parameter can be an object of any class derived from
NumericTable
, except for
PackedTriangularMatrix
,
PackedSymmetricMatrix
, and
CSRNumericTable
.
The recommended data type for storing the steplength sequence is the floatingpoint type, either
float
or
double
, that the algorithm uses in intermediate computations.
 
engine 
SharePtr< engines:: mt19937:: Batch>() 
Pointer to the random number generator engine that is used internally for random choosing terms from the objective function.

Algorithm Output
OptionalDataID

Output
 

correctionPairs 
Numeric table of size 2
m
x
p
where the rows represent correction pairs
s
and
y
. The row
correctionPairs
[
j
], 0 ≤
j
<
m
, is a correction vector
s _{
j}
, and the row
correctionPairs
[
j
],
m
≤
j
< 2
m
, is a correction vector
y _{
j}
.
 
correctionIndices 
Numeric table of size 1 x 2 with 32bit integer indexes. The first value is the index of correction pair
t
, the second value is the index of last iteration
k
from the previous run.
 
averageArgumentLIterations 
Numeric table of size 2 x
p
, where row 0 represents average arguments for previous
L
iterations, and row 1 represents average arguments for last
L
iterations. These values are required to compute
s
correction vectors in the next step. See step
6.b.iii
of the limitedmemory BFGS algorithm.
