Anytime Exploration for Multi-armed Bandits using Confidence Information

We introduce anytime Explore-m, a pure exploration problem for multi-armed bandits (MAB) that requires making a prediction of the top-m arms at every time step. Anytime Explore-m is more practical than fixed budget or fixed confidence formulations of the top-m problem, since many applications involve a finite, but unpredictable, budget. However, the development and analysis of anytime algorithms present many challenges. We propose AT-LUCB (AnyTime Lower and Upper Confidence Bound), the first nontrivial algorithm that provably solves anytime Explore-m. Our analysis shows that the sample complexity of AT-LUCB is competitive to anytime variants of existing algorithms. Moreover, our empirical evaluation on AT-LUCB shows that AT-LUCB performs as well as or better than state-of-the-art baseline methods for anytime Explore-m.