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Gradient descent with adaptive learning rate backpropagation


net.trainFcn = 'traingda' sets the network trainFcn property.

[trainedNet,tr] = train(net,...) trains the network with traingda.

traingda is a network training function that updates weight and bias values according to gradient descent with adaptive learning rate.

Training occurs according to traingda training parameters, shown here with their default values:

  • net.trainParam.epochs — Maximum number of epochs to train. The default value is 1000.

  • net.trainParam.goal — Performance goal. The default value is 0.

  • — Learning rate. The default value is 0.01.

  • net.trainParam.lr_inc — Ratio to increase learning rate. The default value is 1.05.

  • net.trainParam.lr_dec — Ratio to decrease learning rate. The default value is 0.7.

  • net.trainParam.max_fail — Maximum validation failures. The default value is 6.

  • net.trainParam.max_perf_inc — Maximum performance increase. The default value is 1.04.

  • net.trainParam.min_grad — Minimum performance gradient. The default value is 1e-5.

  • — Epochs between displays (NaN for no displays). The default value is 25.

  • net.trainParam.showCommandLine — Generate command-line output. The default value is false.

  • net.trainParam.showWindow — Show training GUI. The default value is true.

  • net.trainParam.time — Maximum time to train in seconds. The default value is inf.

Input Arguments

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Input network, specified as a network object. To create a network object, use for example, feedforwardnet or narxnet.

Output Arguments

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Trained network, returned as a network object..

Training record (epoch and perf), returned as a structure whose fields depend on the network training function (net.NET.trainFcn). It can include fields such as:

  • Training, data division, and performance functions and parameters

  • Data division indices for training, validation and test sets

  • Data division masks for training validation and test sets

  • Number of epochs (num_epochs) and the best epoch (best_epoch).

  • A list of training state names (states).

  • Fields for each state name recording its value throughout training

  • Performances of the best network (best_perf, best_vperf, best_tperf)

More About

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Network Use

You can create a standard network that uses traingda with feedforwardnet or cascadeforwardnet. To prepare a custom network to be trained with traingda,

  1. Set net.trainFcn to 'traingda'. This sets net.trainParam to traingda’s default parameters.

  2. Set net.trainParam properties to desired values.

In either case, calling train with the resulting network trains the network with traingda.

See help feedforwardnet and help cascadeforwardnet for examples.

Gradient Descent with Adaptive Learning Rate Backpropagation

With standard steepest descent, the learning rate is held constant throughout training. The performance of the algorithm is very sensitive to the proper setting of the learning rate. If the learning rate is set too high, the algorithm can oscillate and become unstable. If the learning rate is too small, the algorithm takes too long to converge. It is not practical to determine the optimal setting for the learning rate before training, and, in fact, the optimal learning rate changes during the training process, as the algorithm moves across the performance surface.

You can improve the performance of the steepest descent algorithm if you allow the learning rate to change during the training process. An adaptive learning rate attempts to keep the learning step size as large as possible while keeping learning stable. The learning rate is made responsive to the complexity of the local error surface.

An adaptive learning rate requires some changes in the training procedure used by traingd. First, the initial network output and error are calculated. At each epoch new weights and biases are calculated using the current learning rate. New outputs and errors are then calculated.

As with momentum, if the new error exceeds the old error by more than a predefined ratio, max_perf_inc (typically 1.04), the new weights and biases are discarded. In addition, the learning rate is decreased (typically by multiplying by lr_dec = 0.7). Otherwise, the new weights, etc., are kept. If the new error is less than the old error, the learning rate is increased (typically by multiplying by lr_inc = 1.05).

This procedure increases the learning rate, but only to the extent that the network can learn without large error increases. Thus, a near-optimal learning rate is obtained for the local terrain. When a larger learning rate could result in stable learning, the learning rate is increased. When the learning rate is too high to guarantee a decrease in error, it is decreased until stable learning resumes.

Backpropagation training with an adaptive learning rate is implemented with the function traingda, which is called just like traingd, except for the additional training parameters max_perf_inc, lr_dec, and lr_inc. Here is how it is called to train the previous two-layer network:

p = [-1 -1 2 2; 0 5 0 5];
t = [-1 -1 1 1];
net = feedforwardnet(3,'traingda'); = 0.05;
net.trainParam.lr_inc = 1.05;
net = train(net,p,t);
y = net(p)


traingda can train any network as long as its weight, net input, and transfer functions have derivative functions.

Backpropagation is used to calculate derivatives of performance dperf with respect to the weight and bias variables X. Each variable is adjusted according to gradient descent:

dX = lr*dperf/dX

At each epoch, if performance decreases toward the goal, then the learning rate is increased by the factor lr_inc. If performance increases by more than the factor max_perf_inc, the learning rate is adjusted by the factor lr_dec and the change that increased the performance is not made.

Training stops when any of these conditions occurs:

  • The maximum number of epochs (repetitions) is reached.

  • The maximum amount of time is exceeded.

  • Performance is minimized to the goal.

  • The performance gradient falls below min_grad.

  • Validation performance (validation error) has increased more than max_fail times since the last time it decreased (when using validation).

Version History

Introduced before R2006a