Daniel@0: Daniel@0: Daniel@0: Daniel@0: Netlab Reference Manual graddesc Daniel@0: Daniel@0: Daniel@0: Daniel@0:

graddesc Daniel@0:

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Daniel@0: Purpose Daniel@0:

Daniel@0: Gradient descent optimization. Daniel@0: Daniel@0:

Daniel@0: Description Daniel@0:

Daniel@0: [x, options, flog, pointlog] = graddesc(f, x, options, gradf) uses Daniel@0: batch gradient descent to find a local minimum of the function Daniel@0: f(x) whose gradient is given by gradf(x). A log of the function values Daniel@0: after each cycle is (optionally) returned in errlog, and a log Daniel@0: of the points visited is (optionally) returned in pointlog. Daniel@0: Daniel@0:

Note that x is a row vector Daniel@0: and f returns a scalar value. Daniel@0: The point at which f has a local minimum Daniel@0: is returned as x. The function value at that point is returned Daniel@0: in options(8). Daniel@0: Daniel@0:

graddesc(f, x, options, gradf, p1, p2, ...) allows Daniel@0: additional arguments to be passed to f() and gradf(). Daniel@0: Daniel@0:

The optional parameters have the following interpretations. Daniel@0: Daniel@0:

options(1) is set to 1 to display error values; also logs error Daniel@0: values in the return argument errlog, and the points visited Daniel@0: in the return argument pointslog. If options(1) is set to 0, Daniel@0: then only warning messages are displayed. If options(1) is -1, Daniel@0: then nothing is displayed. Daniel@0: Daniel@0:

options(2) is the absolute precision required for the value Daniel@0: of x at the solution. If the absolute difference between Daniel@0: the values of x between two successive steps is less than Daniel@0: options(2), then this condition is satisfied. Daniel@0: Daniel@0:

options(3) is a measure of the precision required of the objective Daniel@0: function at the solution. If the absolute difference between the Daniel@0: objective function values between two successive steps is less than Daniel@0: options(3), then this condition is satisfied. Daniel@0: Both this and the previous condition must be Daniel@0: satisfied for termination. Daniel@0: Daniel@0:

options(7) determines the line minimisation method used. If it Daniel@0: is set to 1 then a line minimiser is used (in the direction of the negative Daniel@0: gradient). If it is 0 (the default), then each parameter update Daniel@0: is a fixed multiple (the learning rate) Daniel@0: of the negative gradient added to a fixed multiple (the momentum) of Daniel@0: the previous parameter update. Daniel@0: Daniel@0:

options(9) should be set to 1 to check the user defined gradient Daniel@0: function gradf with gradchek. This is carried out at Daniel@0: the initial parameter vector x. Daniel@0: Daniel@0:

options(10) returns the total number of function evaluations (including Daniel@0: those in any line searches). Daniel@0: Daniel@0:

options(11) returns the total number of gradient evaluations. Daniel@0: Daniel@0:

options(14) is the maximum number of iterations; default 100. Daniel@0: Daniel@0:

options(15) is the precision in parameter space of the line search; Daniel@0: default foptions(2). Daniel@0: Daniel@0:

options(17) is the momentum; default 0.5. It should be scaled by the Daniel@0: inverse of the number of data points. Daniel@0: Daniel@0:

options(18) is the learning rate; default 0.01. It should be Daniel@0: scaled by the inverse of the number of data points. Daniel@0: Daniel@0:

Daniel@0: Examples Daniel@0:

Daniel@0: An example of how this function can be used to train a neural network is: Daniel@0:

Daniel@0: 
Daniel@0: options = zeros(1, 18);
Daniel@0: options(17) = 0.1/size(x, 1);
Daniel@0: net = netopt(net, options, x, t, 'graddesc');
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Daniel@0: Daniel@0: Note how the learning rate is scaled by the number of data points. Daniel@0: Daniel@0:

Daniel@0: See Also Daniel@0:

Daniel@0: conjgrad, linemin, olgd, minbrack, quasinew, scg

Daniel@0: Pages: Daniel@0: Index Daniel@0:

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