## Developer Guide

Contents

The stochastic gradient descent (SGD) algorithm is a special case of an iterative solver. For more details, see Iterative Solver.
The following computation methods are available in
Intel DAAL
for the stochastic gradient descent algorithm:
• Mini-batch.
• A special case of mini-batch used by default.
• Momentum

## Mini-batch method

The mini-batch method (
miniBatch
) of the stochastic gradient descent algorithm [Mu2014] follows the algorithmic framework of an iterative solver with an empty set of intrinsic parameters of the algorithm
S
t
, algorithm-specific transformation
T
defined for the learning rate sequence {
η
t
}
t
=1,...,
nIterations
, conservative sequence {
γ
t
}
t
=1,...,
nIterations
and the number of iterations in the internal loop
L
, algorithm-specific vector U and power d of Lebesgue space defined as follows:
For
l
from 1 until
L
:
1. Update the function argument
Convergence check:

## Default method

The default method (
defaultDense
) is a particular case of the mini-batch method with the batch size
b
=1,
L
=1, and conservative sequence

## Momentum method

The momentum method (
momentum
) of the stochastic gradient descent algorithm [Rumelhart86] follows the algorithmic framework of an iterative solver with the set of intrinsic parameters
S
t
, algorithm-specific transformation
T
defined for the learning rate sequence {
η
t
}
t
=1,...,
nIterations
and momentum parameter
μ ∈
[0,1], and algorithm-specific vector U and power d of Lebesgue space defined as follows:
For the momentum method of the SGD algorithm, the set of intrinsic parameters
S
t
only contains the last update vector
v
t
.
Convergence check:

#### Product and Performance Information

1

Intel's compilers may or may not optimize to the same degree for non-Intel microprocessors for optimizations that are not unique to Intel microprocessors. These optimizations include SSE2, SSE3, and SSSE3 instruction sets and other optimizations. Intel does not guarantee the availability, functionality, or effectiveness of any optimization on microprocessors not manufactured by Intel. Microprocessor-dependent optimizations in this product are intended for use with Intel microprocessors. Certain optimizations not specific to Intel microarchitecture are reserved for Intel microprocessors. Please refer to the applicable product User and Reference Guides for more information regarding the specific instruction sets covered by this notice.

Notice revision #20110804