Cost function for support vector regression
Flat means parallel to the x axis; having a small slope. The smaller w is, the closer f(x) is to b; recall that $f(x) \equiv \left&lt; w, x \right&gt; + b$. One way to think about this is as a form of regularization; the flatter the function, the simpler or more parsimonious it is. This applies to both classification and regression.