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

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, H_h-consistent in the one-stage setting, and (H_r,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.