**Now towards relaxing the realizability assumption.**

Continuing our papaya example, let’s assume that the true labels we got about the papaya from the indisputable function f are no longer indisputably true but are received according to P(Y | X). As you observe the papayas, you get to know about their tastiness. Now because there is no true tastiness labelling function f, f ∉ H and hence there is no realizability assumption. The loss function changes now as we do not have a true labelling function to compare to. The new loss function thus would need to compare it to labels Y that we get upon observing the papaya from the distribution.

Lpxy(h) = P[h(X) ≠ Y]. The true loss of hypothesis h is the probability that the prediction of x according to hypothesis h is not equal to the label Y that we get upon observing the papayas from the distribution. The empirical loss (observed loss based on the number of sample observed) would thus be,