srchgol (Neural Network Toolbox)

One-dimensional minimization using golden section search

Syntax

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

Description

srchgol 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 called the golden section search.

srchgol(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

and returns,

a -- Step size, which minimizes performance

gX -- Gradient at new minimum point

perf -- Performance value at new minimum point

retcode -- Return code, which 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 will have different meanings for different search algorithms. Some may 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 golden section algorithm are:

alpha -- Scale factor, which determines sufficient reduction in perf

bmax -- Largest step size

scale_tol -- Parameter, which 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 it. See traincgf, traincgb, traincgp, trainbfg, 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 an 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)

Examples

Here is a problem consisting of inputs p and targets t that we would like to solve with a network.

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

Here 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 srchgol 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 = 'srchgol';
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 srchgol with newff, newcf, or newelm.

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

Set net.trainFcn to 'traincgf'. This will set net.trainParam to traincgf's default parameters.
Set net.trainParam.searchFcn to 'srchgol'.

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

Algorithm

srchgol locates the minimum of the performance function in the search direction dX, using the golden section search. It is based on the algorithm as described on page 33 of Scales (see reference below).

See Also

srchbac, srchbre, srchcha, srchhyb

References

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

srchcha srchhyb