title: Neural Network - global error affected by heuristic
body: <p>I want to apply neural network in very unusual way (It is a part of my research in master thesis). For this example, assume backpropagation neural network(NN). Also I am not quite sure if this is a correct SO forum, so please redirect me elsewhere if needed. </p>
  
  <p>Lets assume we have an input vector <em>i</em> for NN, output vector <em>o</em> and reference output vector <em>r</em>. Also input and output vector are represented with vector of same length (And in our case, they have same semantic meaning, both are 'some configurations').</p>
  
  <p>In <strong>standard</strong> way our global error is calculated like half of squared distance between reference and output vector for input vector <em>i</em> </p>
  
  <blockquote>
    <p>((1/2)(<em>o</em>-<em>r</em>)^2)</p>
  </blockquote>
  
  <p>In <strong>my case</strong> I do not have a reference output vector <em>r</em>. Instead I do have a function <em>F(o)</em> which rates NN output and returns % of output quality. ( To be more specific its result is a percentage of coverage ). And <strong>finally</strong> to complicate this a bit more, my utility function is not a function F(o), but an increase in coverage between input and output (F(o)-F(i)). How to modify global error funcion in such way that my utility function will be taken into account?.</p>