I have looked at the logistic loss function at many different sources, and many places I find it plotted like shown here:
The logistic loss is typically defined as $L(y_i, f(x_i)) = log(1+exp(x_i y_i))$ where $y_i = \pm \;1$.
What confuses me is that when calculating the logistic loss for $x_i = 0$, I cannot see how to get a value of $1$ when inserting into the formula:
$L(1, f(0)) = L(-1, f(0)) = log(1+exp(0)) \approx 0.69$
Have I misunderstood the concept? I can only see that a loss of $1$ can be returned by using a logarithm with base $1$, but I cannot imagine that would be anyone's intention.