Convexity of 0-1 loss

Question

Problem

The 0-1 loss is defined as $\ell(h(\mathbf{x}), y) = \mathbb{1}_{h(\mathbf{x} \neq y)}$. How could I show the convexity of this loss function?

What I Have Done

I tried to verify the Jensen's inequality with respect to $\ell(h(\mathbf{x}), y)$, but I do not know how to do with the form with indicator function.

Answer 1

I presume you mean the loss is $1$ if $h({\bf x)}=y$ and $0$ if not. This will never be convex except in trivial cases where it is constant.