One-Stage Top-$k$ Learning-to-Defer: Score-Based Surrogates with Theoretical Guarantees

TL;DR

This paper presents a novel one-stage learning-to-defer framework that jointly optimizes prediction and deferral for multiple entities, with theoretical guarantees and adaptive selection of experts, improving over existing single-expert methods.

Contribution

It introduces a unified, score-based, end-to-end approach for Top-$k$ deferral with a new convex surrogate and adaptive variant, enabling flexible and theoretically sound multi-expert deferral.

Findings

Outperforms Top-1 deferral in experiments on CIFAR-10 and SVHN.

The surrogate is Bayes- and $ ext{H}$-consistent under mild assumptions.

Adaptive Top-$k(x)$ balances accuracy and consultation cost effectively.

Abstract

We introduce the first one-stage Top-$k$ Learning-to-Defer framework, which unifies prediction and deferral by learning a shared score-based model that selects the $k$ most cost-effective entities-labels or experts-per input. While existing one-stage L2D methods are limited to deferring to a single expert, our approach jointly optimizes prediction and deferral across multiple entities through a single end-to-end objective. We define a cost-sensitive loss and derive a novel convex surrogate that is independent of the cardinality parameter $k$, enabling generalization across Top-$k$ regimes without retraining. Our formulation recovers the Top-1 deferral policy of prior score-based methods as a special case, and we prove that our surrogate is both Bayes-consistent and $\mathcal{H}$-consistent under mild assumptions. We further introduce an adaptive variant, Top-$k(x)$, which dynamically selects the number of consulted entities per input to balance predictive accuracy and consultation cost. Experiments on CIFAR-10 and SVHN confirm that our one-stage Top-$k$ method strictly outperforms Top-1 deferral, while Top-$k(x)$ achieves superior accuracy-cost trade-offs by tailoring allocations to input complexity.