See Figure 1 for an illustration of the different SNR thresholds and Section 2.1 for more

This perspectiveparallels an earlier phenomenon inthe much better understood field of optimization where convexity has played a preponderant role for both theoretical and methodological advances [Nes04; Bub15].

However,the criteria by which the prediction model is trained are often inconsistent with the goal of the downstream optimization problem. Recently, decision-focused prediction approaches, such as SPO+ and direct optimization, have been proposed to fill this gap. However, they cannot directly handle the soft constraints with the max operator required in many real-world objectives.

Quantifying uncertainty is important for actionable predictions in real-world applications.

Figure 1: The thick line in (a) indicates minimal pointsofC.Thethicklinein(b)indicatesweakly minimalpointsofC.