srchhyb :: Functions (Neural Network Toolbox™)

srchhyb

Purpose

1-D minimization using a hybrid bisection-cubic search

Syntax

[a,gX,perf,retcode,delta,tol] = 
srchhyb(net,X,Pd,Tl,Ai,Q,TS,dX,gX,perf,dperf,delta,tol,ch_perf)

Description

srchhyb is a linear search routine. It searches in a given direction to locate the minimum of the performance function in that direction. It uses a technique that is a combination of a bisection and a cubic interpolation.

srchhyb(net,X,Pd,Tl,Ai,Q,TS,dX,gX,perf,dperf,delta,tol,ch_perf) takes these inputs,

net
Neural network

X
Vector containing current values of weights and biases

Pd
Delayed input vectors

Tl
Layer target vectors

Ai
Initial input delay conditions

Q
Batch size

TS
Time steps

dX
Search direction vector

gX
Gradient vector

perf
Performance value at current X

dperf
Slope of performance value at current X in direction of dX

delta
Initial step size

tol
Tolerance on search

ch_perf
Change in performance on previous step

`net`	Neural network
`X`	Vector containing current values of weights and biases
`Pd`	Delayed input vectors
`Tl`	Layer target vectors
`Ai`	Initial input delay conditions
`Q`	Batch size
`TS`	Time steps
`dX`	Search direction vector
`gX`	Gradient vector
`perf`	Performance value at current `X`
`dperf`	Slope of performance value at current `X` in direction of `dX`
`delta`	Initial step size
`tol`	Tolerance on search
`ch_perf`	Change in performance on previous step

and returns

a
Step size that minimizes performance

gX
Gradient at new minimum point

perf
Performance value at new minimum point

retcode
Return code that has three elements. The first two elements correspond to the number of function evaluations in the two stages of the search. The third element is a return code. These have different meanings for different search algorithms. Some might not be used in this function.

0
Normal

1
Minimum step taken

2
Maximum step taken

3
Beta condition not met

delta
New initial step size, based on the current step size

tol
New tolerance on search

`a`	Step size that minimizes performance
`gX`	Gradient at new minimum point
`perf`	Performance value at new minimum point
`retcode`	Return code that has three elements. The first two elements correspond to the number of function evaluations in the two stages of the search. The third element is a return code. These have different meanings for different search algorithms. Some might not be used in this function.
	`0`	Normal
	`1`	Minimum step taken
	`2`	Maximum step taken
	`3`	Beta condition not met
`delta`	New initial step size, based on the current step size
`tol`	New tolerance on search

Parameters used for the hybrid bisection-cubic algorithm are

alpha
Scale factor that determines sufficient reduction in perf

beta
Scale factor that determines sufficiently large step size

bmax
Largest step size

scale_tol
Parameter that relates the tolerance tol to the initial step size delta, usually set to 20

`alpha`	Scale factor that determines sufficient reduction in `perf`
`beta`	Scale factor that determines sufficiently large step size
`bmax`	Largest step size
`scale_tol`	Parameter that relates the tolerance `tol` to the initial step size `delta`, usually set to 20

The defaults for these parameters are set in the training function that calls them. See traincgf, traincgb, traincgp, trainbfg, and trainoss.

Dimensions for these variables are

Pd
No x Ni x TS cell array
Each element P{i,j,ts} is a Dij x Q matrix.

Tl
Nl x TS cell array
Each element P{i,ts} is a Vi x Q matrix.

Ai
Nl x LD cell array
Each element Ai{i,k} is an Si x Q matrix.

`Pd`	`No` x `Ni` x `TS` cell array	Each element `P{i,j,ts}` is a `Dij` x `Q` matrix.
`Tl`	`Nl` x `TS` cell array	Each element `P{i,ts}` is a `Vi` x `Q` matrix.
`Ai`	`Nl` x `LD` cell array	Each element `Ai{i,k}` is an `Si` x `Q` matrix.

where

Ni
=

net.numInputs

Nl
=

net.numLayers

LD
=

net.numLayerDelays

Ri
=

net.inputs{i}.size

Si
=

net.layers{i}.size

Vi
=

net.targets{i}.size

Dij
=

Ri * length(net.inputWeights{i,j}.delays)

`Ni`	`=`	`net.numInputs`
`Nl`	`=`	`net.numLayers`
`LD`	`=`	`net.numLayerDelays`
`Ri`	`=`	`net.inputs{i}.size`
`Si`	`=`	`net.layers{i}.size`
`Vi`	`=`	`net.targets{i}.size`
`Dij`	`=`	`Ri * length(net.inputWeights{i,j}.delays)`

Examples

Here is a problem consisting of inputs p and targets t to be solved with a network.

```
p = [0 1 2 3 4 5];
t = [0 0 0 1 1 1];
```

A two-layer feed-forward network is created. The network's input ranges from [0 to 10]. The first layer has two tansig neurons, and the second layer has one logsig neuron. The traincgf network training function and the srchhyb search function are to be used.

Create and Test a Network

net = newff([0 5],[2 1],{'tansig','logsig'},'traincgf');
a = sim(net,p)

Train and Retest the Network
net.trainParam.searchFcn = 'srchhyb';
net.trainParam.epochs = 50;
net.trainParam.show = 10;
net.trainParam.goal = 0.1;
net = train(net,p,t);
a = sim(net,p)

Network Use

You can create a standard network that uses srchhyb with newff, newcf, or newelm.

To prepare a custom network to be trained with traincgf, using the line search function srchhyb,

Set net.trainFcn to 'traincgf'. This sets net.trainParam to traincgf's default parameters.
Set net.trainParam.searchFcn to 'srchhyb'.

The srchhyb function can be used with any of the following training functions: traincgf, traincgb, traincgp, trainbfg, trainoss.

Algorithm

srchhyb locates the minimum of the performance function in the search direction dX, using the hybrid bisection-cubic interpolation algorithm described on page 50 of Scales (see reference below).

Reference

Scales, L.E., Introduction to Non-Linear Optimization, New York Springer-Verlag, 1985