Why Ask One When You Can Ask $k$? Learning-to-Defer to the Top-$k$ Experts

• URL: http://arxiv.org/abs/2504.12988v4
• Date: Mon, 13 Oct 2025 03:36:20 GMT
• Title: Why Ask One When You Can Ask $k$? Learning-to-Defer to the Top-$k$ Experts
• Authors: Yannis Montreuil, Axel Carlier, Lai Xing Ng, Wei Tsang Ooi,
• Abstract summary: We introduce the first framework for Top-$k$ Learning-to-Defer.<n>It allocates queries to the $k$ most cost-effective entities.<n>We also propose Top-$k(x)$ Learning-to-Defer, an adaptive variant that learns the optimal number of experts per query.
• Score: 6.792743621449621
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Existing Learning-to-Defer (L2D) frameworks are limited to single-expert deferral, forcing each query to rely on only one expert and preventing the use of collective expertise. We introduce the first framework for Top-$k$ Learning-to-Defer, which allocates queries to the $k$ most cost-effective entities. Our formulation unifies and strictly generalizes prior approaches, including the one-stage and two-stage regimes, selective prediction, and classical cascades. In particular, it recovers the usual Top-1 deferral rule as a special case while enabling principled collaboration with multiple experts when $k>1$. We further propose Top-$k(x)$ Learning-to-Defer, an adaptive variant that learns the optimal number of experts per query based on input difficulty, expert quality, and consultation cost. To enable practical learning, we develop a novel surrogate loss that is Bayes-consistent, $\mathcal{H}_h$-consistent in the one-stage setting, and $(\mathcal{H}_r,\mathcal{H}_g)$-consistent in the two-stage setting. Crucially, this surrogate is independent of $k$, allowing a single policy to be learned once and deployed flexibly across $k$. Experiments across both regimes show that Top-$k$ and Top-$k(x)$ deliver superior accuracy-cost trade-offs, opening a new direction for multi-expert deferral in L2D.

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