  In this paper, we consider the distributed stochastic multi-armed bandit
problem, where a global arm set can be accessed by multiple players
independently. The players are allowed to exchange their history of
observations with each other at specific points in time. We study the
relationship between regret and communication. When the time horizon is known,
we propose the Over-Exploration strategy, which only requires one-round
communication and whose regret does not scale with the number of players. When
the time horizon is unknown, we measure the frequency of communication through
a new notion called the density of the communication set, and give an exact
characterization of the interplay between regret and communication.
Specifically, a lower bound is established and stable strategies that match the
lower bound are developed. The results and analyses in this paper are specific
but can be translated into more general settings.
