# Cost function for adaptive algorithms

I am having little difficulty to understand that why most of the adaptive algorithms use error power or addition of error power as cost function/minimization criterion. I have read that minimization of error power criterion gives us best results from estimation mean point of view. I am not being able to grasp that either. So can someone please tell me in simple language what are the actual reasons to use above criterion? Why cant we simply use error as the minimization criterion?

• Using only the error values (i.e. deviations from measurement to the model) won't work, since individual deviation values can cancel each other out. Example: Imagine one period of a sine wave, sampled equidistantly and symmetrically at an odd number of points). If you compare this to the correct model function (said sine wave), your summed up error between the model and the data will be zero as it should. If you would multiply your model by $-1$ (or introduce an $180^\circ$ shift and compare it to the data, the model will completely fail to explain the data, but will have a error sum 0, too. – M529 Mar 12 '16 at 14:14

In very simple words: error, directly, cannot be used as a criterion. You can minimize a signed function to $-\infty$, which is not really useful here. As least, you need a cost function with a lower bound.