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：现有学习推迟框架局限于单专家模式，每个查询仅能依赖单一专家，无法利用集体智慧。我们提出首个Top-$k$学习推迟框架，该框架能将查询分配给成本效益最优的$k$个实体。该形式统一并严格扩展了现有方法，涵盖单阶段与两阶段模式、选择性预测及经典级联结构。特别地，当$k=1$时恢复经典Top-1推迟规则，而$k>1$时则实现与多专家的原则性协作。我们进一步提出自适应变体Top-$k(x)$学习推迟，能根据输入难度、专家质量及咨询成本自适应学习每个查询所需的最佳专家数量。为实现实用化训练，我们开发了新型代理损失函数，该函数在贝叶斯意义上一致，在单阶段设置中满足$\mathcal{H}_h$一致性，在两阶段设置中满足($\mathcal{H}_r,\mathcal{H}_g$)一致性。关键创新在于该代理损失与$k$无关，使得单一策略模型可一次训练并灵活部署于任意$k$值。跨双阶段模型的实验表明，Top-$k$及Top-$k(x)$实现了更优的精度-成本权衡，为L2D领域的多专家推迟开辟了新方向。