  We propose a novel modification of the standard upper confidence bound (UCB)
method for the stochastic multi-armed bandit (MAB) problem which tunes the
confidence bound of a given bandit based on its distance to others. Our UCB
distance tuning (UCB-DT) formulation enables improved performance as measured
by expected regret by preventing the MAB algorithm from focusing on non-optimal
bandits which is a well-known deficiency of standard UCB. "Distance tuning" of
the standard UCB is done using a proposed distance measure, which we call
bandit distance, that is parameterizable and which therefore can be optimized
to control the transition rate from exploration to exploitation based on
problem requirements. We empirically demonstrate increased performance of
UCB-DT versus many existing state-of-the-art methods which use the UCB
formulation for the MAB problem. Our contribution also includes the development
of a conceptual tool called the "Exploration Bargain Point" which gives
insights into the tradeoffs between exploration and exploitation. We argue that
the Exploration Bargain Point provides an intuitive perspective that is useful
for comparatively analyzing the performance of UCB-based methods.
