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

Abstract

Although existing Learning-to-Defer (L2D) frameworks support multiple experts, they allocate each query to a single expert, limiting their ability to leverage collective expertise in complex decision-making scenarios. To address this, we introduce the first framework for Top-k Learning-to-Defer, enabling systems to defer each query to the k most cost-effective experts. Our formulation strictly generalizes classical two-stage L2D by supporting multi-expert deferral-a capability absent in prior work. We further propose Top-k(x) Learning-to-Defer, an adaptive extension that learns the optimal number of experts per query based on input complexity, expert quality, and consultation cost. We introduce a novel surrogate loss that is Bayes-consistent, (R, G)-consistent, and independent of the cardinality parameter k, enabling efficient reuse across different values of k. We show that classical model cascades arise as a special case of our method, situating our framework as a strict generalization of both selective deferral and cascaded inference. Experiments on classification and regression demonstrate that Top-k and Top-k(x) yield improved accuracy--cost trade-offs, establishing a new direction for multi-expert deferral in Learning-to-Defer.

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