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

• URL: http://arxiv.org/abs/2504.12988v2
• Date: Tue, 22 Apr 2025 07:02:20 GMT
• Title: Why Ask One When You Can Ask $k$? Two-Stage Learning-to-Defer to the Top-$k$ Experts
• Authors: Yannis Montreuil, Axel Carlier, Lai Xing Ng, Wei Tsang Ooi,
• Abstract summary: Learning-to-Defer (L2D) enables decision-making systems to improve reliability by selectively deferring uncertain predictions to more competent agents.<n>We propose Top-$k$ Learning-to-Defer, a generalization of the classical two-stage L2D framework that allocates each query to the $k$ most confident agents instead of a single one.<n>To further enhance flexibility and cost-efficiency, we introduce Top-$k(x)$ Learning-to-Defer, an adaptive extension that learns the optimal number of agents to consult for each query.
• Score: 3.6787328174619254
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Learning-to-Defer (L2D) enables decision-making systems to improve reliability by selectively deferring uncertain predictions to more competent agents. However, most existing approaches focus exclusively on single-agent deferral, which is often inadequate in high-stakes scenarios that require collective expertise. We propose Top-$k$ Learning-to-Defer, a generalization of the classical two-stage L2D framework that allocates each query to the $k$ most confident agents instead of a single one. To further enhance flexibility and cost-efficiency, we introduce Top-$k(x)$ Learning-to-Defer, an adaptive extension that learns the optimal number of agents to consult for each query, based on input complexity, agent competency distributions, and consultation costs. For both settings, we derive a novel surrogate loss and prove that it is Bayes-consistent and $(\mathcal{R}, \mathcal{G})$-consistent, ensuring convergence to the Bayes-optimal allocation. Notably, we show that the well-established model cascades paradigm arises as a restricted instance of our Top-$k$ and Top-$k(x)$ formulations. Extensive experiments across diverse benchmarks demonstrate the effectiveness of our framework on both classification and regression tasks.

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