## Resilient backpropagation (Rprop) optimization algorithm

### Description

From Riedmiller (1994): Rprop stands for 'Resilient backpropagation' and is a local adaptive learning scheme. The basic principle of Rprop is to eliminate the harmful influence of the size of the partial derivative on the weight step. As a consequence, only the sign of the derivative is considered to indicate the direction of the weight update. The size of the weight change is exclusively determined by a weight-specific, so called 'update-value'.

This function implements the iRprop+ algorithm from Igel and Huesken (2003).

### Usage

rprop(w, f, iterlim = 100, print.level = 1, delta.0 = 0.1,
delta.min = 1e-06, delta.max = 50, epsilon = 1e-08,
step.tol = 1e-06, f.target = -Inf, ...)


### Arguments

 w the starting parameters for the minimization. f the function to be minimized. If the function value has an attribute called gradient, this will be used in the calculation of updated parameter values. Otherwise, numerical derivatives will be used. iterlim the maximum number of iterations before the optimization is stopped. print.level the level of printing which is done during optimization. A value of 0 suppresses any progress reporting, whereas positive values report the value of f and the mean change in f over the previous three iterations. delta.0 size of the initial Rprop update-value. delta.min minimum value for the adaptive Rprop update-value. delta.max maximum value for the adaptive Rprop update-value. epsilon step-size used in the finite difference calculation of the gradient. step.tol convergence criterion. Optimization will stop if the change in f over the previous three iterations falls below this value. f.target target value of f. Optimization will stop if f falls below this value. ... further arguments to be passed to f.

### Value

A list with elements:

 par The best set of parameters found. value The value of f corresponding to par. gradient An estimate of the gradient at the solution found.

### References

Igel, C. and M. Huesken, 2003. Empirical evaluation of the improved Rprop learning algorithms. Neurocomputing 50: 105-123.

Riedmiller, M., 1994. Advanced supervised learning in multilayer perceptrons - from backpropagation to adaptive learning techniques. Computer Standards and Interfaces 16(3): 265-278.