  We study the stochastic Budgeted Multi-Armed Bandit (MAB) problem, where a
player chooses from $K$ arms with unknown expected rewards and costs. The goal
is to maximize the total reward under a budget constraint. A player thus seeks
to choose the arm with the highest reward-cost ratio as often as possible.
Current state-of-the-art policies for this problem have several issues, which
we illustrate. To overcome them, we propose a new upper confidence bound (UCB)
sampling policy, $\omega$-UCB, that uses asymmetric confidence intervals. These
intervals scale with the distance between the sample mean and the bounds of a
random variable, yielding a more accurate and tight estimation of the
reward-cost ratio compared to our competitors. We show that our approach has
logarithmic regret and consistently outperforms existing policies in synthetic
and real settings.
