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.

翻译：现有学习赋权（Learning-to-Defer, L2D）框架受限，仅支持向单个专家赋权，导致每个查询仅能依赖单一专家，无法利用集体专长。我们提出了首个面向Top-$k$学习赋权的框架，该框架将查询分配给成本效益最优的$k$个实体。本文公式统一并严格泛化了先前方法，包括单阶段与两阶段机制、选择性预测以及经典级联模型。特别地，该框架将常规Top-1赋权规则作为特例恢复，并在$k>1$时实现了与多专家的原则性协作。我们进一步提出自适应变体Top-$k(x)$学习赋权，其能根据输入难度、专家质量及咨询成本，为每个查询学习最优的赋权专家数量。为支持实际学习，我们开发了一种新的替代损失函数，该函数在单阶段设置中满足贝叶斯一致性及$\mathcal{H}_h$-一致性，在两阶段设置中满足$(\mathcal{H}_r,\mathcal{H}_g)$-一致性。关键是，该替代函数与$k$无关，使得单一策略可一次性学习并灵活部署于不同$k$值。跨两种机制的实验表明，Top-$k$与Top-$k(x)$实现了优越的精度-成本权衡，为L2D中的多专家赋权开辟了新方向。