This paper studies the sample complexity (aka number of comparisons) bounds\nfor the active best-$k$ items selection from pairwise comparisons. From a given\nset of items, the learner can make pairwise comparisons on every pair of items,\nand each comparison returns an independent noisy result about the preferred\nitem. At any time, the learner can adaptively choose a pair of items to compare\naccording to past observations (i.e., active learning). The learner's goal is\nto find the (approximately) best-$k$ items with a given confidence, while\ntrying to use as few comparisons as possible. In this paper, we study two\nproblems: (i) finding the probably approximately correct (PAC) best-$k$ items\nand (ii) finding the exact best-$k$ items, both under strong stochastic\ntransitivity and stochastic triangle inequality. For PAC best-$k$ items\nselection, we first show a lower bound and then propose an algorithm whose\nsample complexity upper bound matches the lower bound up to a constant factor.\nFor the exact best-$k$ items selection, we first prove a worst-instance lower\nbound. We then propose two algorithms based on our PAC best items selection\nalgorithms: one works for $k=1$ and is sample complexity optimal up to a loglog\nfactor, and the other works for all values of $k$ and is sample complexity\noptimal up to a log factor.\n