Cost function adaptation revisited

A variety of related stochastic gradient algorithms can be specified by modifying the minimum mean square error cost function. A part of them have been previously known as cost function adaptation algorithms, though they actually have implemented a kind of variable error exponent algorithms. Besides, the adaptive filtering literature contains many variable step-size methods. In this paper we reconsider former cost function adaptation algorithms and the goal is to integrate variable error exponent and variable step-size algorithms into a unifying framework, i.e. cost function adaptation algorithms. Finally some comments on implementation of variable error-exponents are delivered.