Logistic loss

For a signed margin $u=yh(x)$, the logistic loss isIt is convex and has derivative ${\varphi }^{\prime }(u)=-e^{-u}/(1+e^{-u})$.

For a positive semidefinite trace ball ${\mathcal{S}}_s$, the quadratic-form hypothesis class isIts empirical logistic risk is convex as a function of $M$.