Parametrized Stochastic Multi-armed Bandits with Binary Rewards

In this paper, we consider the problem of multi armed bandits with a large number of correlated arms. We assume that the arms have Bernoulli distributed rewards, independent across time, where the probabilities of success are parametrized by known attribute vectors for each arm, as well as an unknown preference vector, each of dimension n. For this model, we seek an algorithm with a total regret that is sub-linear in time and independent of the number of arms. We present such an algorithm, which we call the Three-phase Algorithm, and analyze its performance. We show an upper bound on the total regret which applies uniformly in time. The asymptotics of this bound show that for any f ∈ ω(log(T)), the total regret can be made to be O(n·f(T)), independent of the number of arms.