One-Stage Top-$k$ Learning-to-Defer: Score-Based Surrogates with Theoretical Guarantees
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908588527583232 |
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| author | Montreuil, Yannis Carlier, Axel Ng, Lai Xing Ooi, Wei Tsang |
| author_facet | Montreuil, Yannis Carlier, Axel Ng, Lai Xing Ooi, Wei Tsang |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_10160 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | One-Stage Top-$k$ Learning-to-Defer: Score-Based Surrogates with Theoretical Guarantees Montreuil, Yannis Carlier, Axel Ng, Lai Xing Ooi, Wei Tsang Machine Learning 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. |
| title | One-Stage Top-$k$ Learning-to-Defer: Score-Based Surrogates with Theoretical Guarantees |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2505.10160 |