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.

翻译：我们提出了一种新型损失函数，用于最小化基于机器学习的资源分配系统的中断概率。单用户多资源贪婪分配策略构成了我们的应用场景，其中ML二分类预测器辅助选择满足既定中断判据的资源。虽然其他资源分配策略可能适用，但并非本研究的重点。我们的核心目标是在理论上开发该损失函数，并利用其训练ML模型以解决中断概率挑战。由于无法获取未来信道状态信息，该预测器需预见每个资源未来可能的中断状态。当预测器判定某资源可能满足要求时，便将其分配给用户。我们的主要成果建立了该系统中断概率的精确及渐近表达式。这些表达式表明：若仅优化以ML预测器推荐资源分配为条件的单资源中断概率（看似最直接的方法），可能导致预测器拒绝所有资源。研究还表明，关注准确率、假阳性率或召回率等标准指标可能无法产生最优预测器。基于此结果，我们构建了一个理论最优的可微损失函数来训练预测器。我们随后比较了使用该损失函数与传统损失函数（二分类交叉熵BCE、均方误差MSE、平均绝对误差MAE）训练的预测器。在所有场景中，采用新型损失函数训练的预测器均展现出更优的中断概率性能。在某些情况下，我们的损失函数相较于BCE、MAE和MSE训练的预测器，性能提升达数个数量级。