Consider the online learning setting where instantaneous loss is given by \begin{equation} \ell_t(f_t;(\mathbf{x}_t,y_t))=\max \left( {0,\left( \left( {\frac{N}{P}} \right){I_{(y_t = 1)}} + \left( {\frac{{P - F_n}}{P}} \right){I_{(y_t = - 1)}}\right) - y_t f_t({\bf x}_t) } \right) \end{equation}
where $\ell_t$ is instantaneous loss at time $t$; $({\bf x}_t,y_t) \subseteq R^n \times \{-1,+1\}$ is instance-label pair. $N$ and $P$ denote the count of negative and positive instances respectively and and $F_n$ is no. of false negatives so far.
Can somebody tell me if the loss function is convex?