New algorithm optimally identifies top items from noisy comparisons

Researchers Motti Goldberger and Nils Rudi have published a paper at ICML 2026 that introduces the first asymptotically optimal algorithm for the fixed-confidence top-k identification problem from noisy pairwise comparisons. In this setting, an algorithm sequentially selects pairs of items to compare, observes noisy outcomes, and must stop with a set of top-k items that is correct with probability at least 1−δ. The central challenge is minimizing the expected number of comparisons (sample complexity) while satisfying the error constraint. Prior work achieved asymptotic optimality for many bandit pure-exploration problems, but for top-k identification under latent utility models—even for top-1—no such algorithm existed.

The authors characterize the information-theoretic lower bound as a saddle-point problem and develop a computationally efficient primal-dual procedure that learns the asymptotically optimal allocation of comparisons online. Their adaptive algorithm tracks this allocation and provably matches the lower bound as δ→0. This breakthrough has immediate applications in ranking, recommendation systems, A/B testing, and any domain where we need to identify top performers from noisy pairwise data. The paper is available on arXiv under ID 2607.08979.