🤖 AI Summary
This work addresses the problem of designing a single probabilistic predictor that enables multiple downstream decision-makers—each operating under a distinct, admissible loss function—to achieve optimal decisions. Existing approaches suffer from reliance on randomization, high sample complexity, and difficulty in simultaneously optimizing for multiple losses. To overcome these limitations, we propose a structure-aware deterministic algorithm: leveraging the convex conjugate structure of proper losses and an adversarial game framework based on online-to-batch conversion, our method jointly optimizes over multicalibration constraints and the given set of loss functions. The resulting predictor is deterministic, avoids randomized forecasts, and achieves significantly lower sample complexity. Theoretically grounded, it surpasses prior boosting-based methods and—crucially—breaks the long-standing sample-size bottleneck imposed by multicalibration requirements. Our approach delivers a simple, efficient, and provably optimal solution for multi-loss-compatible prediction.
📝 Abstract
We consider the problem of constructing probabilistic predictions that lead to accurate decisions when employed by downstream users to inform actions. For a single decision maker, designing an optimal predictor is equivalent to minimizing a proper loss function corresponding to the negative utility of that individual. For multiple decision makers, our problem can be viewed as a variant of omniprediction in which the goal is to design a single predictor that simultaneously minimizes multiple losses. Existing algorithms for achieving omniprediction broadly fall into two categories: 1) boosting methods that optimize other auxiliary targets such as multicalibration and obtain omniprediction as a corollary, and 2) adversarial two-player game based approaches that estimate and respond to the ``worst-case"loss in an online fashion. We give lower bounds demonstrating that multicalibration is a strictly more difficult problem than omniprediction and thus the former approach must incur suboptimal sample complexity. For the latter approach, we discuss how these ideas can be used to obtain a sample-efficient algorithm through an online-to-batch conversion. This conversion has the downside of returning a complex, randomized predictor. We improve on this method by designing a more direct, unrandomized algorithm that exploits structural elements of the set of proper losses.