If also ants are able...

Abstract

Learning, as a single value inference facility is unavoidably connected with an optimization problem. You fix a cost function compliant with your probability model, if any, and look for a solution in the parameter space that minimizes the function up to a given approximation. You search in the parameter space since you want to assess a function to be profitably used in the variable space. Otherwise you may be interested in optimizing a given function directly in the variable space. A typical example where the two optimization targets are in symbiosis is represented by the Boltzmann machines. You move along the increasing direction of the function (8.24) with the machine updating its state according to (8.22). When you are close to the maximum of this function you are close to the equilibrium, hence you may collect statistics feeding the learning rule in the parameter space. As a matter of fact, many optimization techniques do not change when you move from one space to the other, and we often speak of learning facility even when we are optimizing in the variable space. Actually with the same GA techniques you may learn the best fitting function by working on its code, like with the chromosome sequence determining our proteins. Thus learning is coming to achieve the widest acceptance of emergence of functionality, possibly specific - as the ability of optimizing a given function - possibly broad-band - as the ability of assessing an optimal function. © 2008 Springer-Verlag Berlin Heidelberg.