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

arXiv: https://arxiv.org/abs/2505.10160 · HTML: https://mlsanity.com/paper/2505.10160/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- First posted on arXiv 15 May 2025.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Built on by (most cited first, 4 of 4)

- [Mastering Multiple-Expert Routing: Realizable H-Consistency and Strong Guarantees for Learning to Defer](https://mlsanity.com/paper/2506.20650/) (2025)
- [Budgeted Multiple-Expert Deferral](https://mlsanity.com/paper/2510.26706/) (2025)
- [Principled Algorithms for Optimizing Generalized Metrics in Binary Classification](https://mlsanity.com/paper/2512.23133/) (2025)
- [Adversarial Robustness in One-Stage Learning-to-Defer](https://mlsanity.com/paper/2510.10988/) (2025)

## Abstract (arXiv)

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 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.