Panprediction: Optimal Predictions for Any Downstream Task and Loss

TL;DR

This paper introduces panprediction, a unified framework for training models capable of minimizing many losses across numerous downstream tasks, with algorithms that are statistically efficient and improve existing guarantees.

Contribution

It formalizes the panprediction paradigm, develops algorithms with optimal sample complexities, and connects panprediction to calibration techniques, advancing the theoretical understanding of multi-task learning.

Findings

Algorithms for deterministic and randomized panpredictors with optimal sample complexities.

Simultaneous minimization of infinitely many losses is statistically as easy as single-task minimization.

Improved sample complexity bounds for omniprediction and multi-group learning.

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 $\tilde{O}(1/\varepsilon^3)$ and $\tilde{O}(1/\varepsilon^2)$ 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.