Panprediction: Optimal Predictions for Any Downstream Task and Loss

2025-10-31

AI Summary

This paper studies learning a universal predictor from limited data that adapts to arbitrary downstream tasks and loss functions—termed *panprediction*. To this end, we propose the first unified framework for joint generalization across both multiple tasks and multiple losses, reducing panprediction to *step calibration*, thereby achieving statistical complexity nearly matching the theoretical lower bound for single-task, single-loss learning. Our method integrates deterministic and randomized algorithmic designs and introduces a near-lossless reduction technique. As a result, it requires only $ ilde{O}(1/varepsilon^3)$ and $ ilde{O}(1/varepsilon^2)$ samples to learn deterministic and randomized panpredictors, respectively—substantially improving upon the sample complexity of prior omniprediction approaches. This work establishes an efficient, scalable theoretical and algorithmic foundation for generalized predictive modeling.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Learning to Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization

Abstract

Supervised learning is classically formulated as training a model to minimize a fixed loss function over a fixed distribution, or task. However, an emerging paradigm instead views model training as extracting enough information from data so that the model can be used to minimize many losses on many downstream tasks. We formalize a mathematical framework for this paradigm, which we call panprediction, and study its statistical complexity. Formally, panprediction generalizes omniprediction and sits upstream from multi-group learning, which respectively focus on predictions that generalize to many downstream losses or many downstream tasks, but not both. Concretely, we design algorithms that learn deterministic and randomized panpredictors with $ ilde{O}(1/varepsilon^3)$ and $ ilde{O}(1/varepsilon^2)$ samples, respectively. Our results demonstrate that under mild assumptions, simultaneously minimizing infinitely many losses on infinitely many tasks can be as statistically easy as minimizing one loss on one task. Along the way, we improve the best known sample complexity guarantee of deterministic omniprediction by a factor of $1/varepsilon$, and match all other known sample complexity guarantees of omniprediction and multi-group learning. Our key technical ingredient is a nearly lossless reduction from panprediction to a statistically efficient notion of calibration, called step calibration.

Problem

• Generalizing predictions for multiple downstream tasks and losses
• Developing algorithms for efficient panpredictor sample complexity
• Establishing statistical equivalence between single and multi-task learning

Innovation

• Panprediction framework for multiple downstream tasks
• Algorithms with improved sample complexity guarantees
• Reduction from panprediction to step calibration