  We introduce a novel loss function to minimize the outage probability of an
ML-based resource allocation system. A single-user multi-resource greedy
allocation strategy constitutes our application scenario, for which an ML
binary classification predictor assists in selecting a resource satisfying the
established outage criterium. While other resource allocation policies may be
suitable, they are not the focus of our study. Instead, our primary emphasis is
on theoretically developing this loss function and leveraging it to train an ML
model to address the outage probability challenge. With no access to future
channel state information, this predictor foresees each resource's likely
future outage status. When the predictor encounters a resource it believes will
be satisfactory, it allocates it to the user. Our main result establishes exact
and asymptotic expressions for this system's outage probability. These
expressions reveal that focusing solely on the optimization of the per-resource
outage probability conditioned on the ML predictor recommending resource
allocation (a strategy that appears to be most appropriate) may produce
inadequate predictors that reject every resource. They also reveal that
focusing on standard metrics, like precision, false-positive rate, or recall,
may not produce optimal predictors. With our result, we formulate a
theoretically optimal, differentiable loss function to train our predictor. We
then compare predictors trained using this and traditional loss functions
namely, binary cross-entropy (BCE), mean squared error (MSE), and mean absolute
error (MAE). In all scenarios, predictors trained using our novel loss function
provide superior outage probability performance. Moreover, in some cases, our
loss function outperforms predictors trained with BCE, MAE, and MSE by multiple
orders of magnitude.
