  We study exploration in Multi-Armed Bandits in a setting where $k$ players
collaborate in order to identify an $\epsilon$-optimal arm. Our motivation
comes from recent employment of bandit algorithms in computationally intensive,
large-scale applications. Our results demonstrate a non-trivial tradeoff
between the number of arm pulls required by each of the players, and the amount
of communication between them. In particular, our main result shows that by
allowing the $k$ players to communicate only once, they are able to learn
$\sqrt{k}$ times faster than a single player. That is, distributing learning to
$k$ players gives rise to a factor $\sqrt{k}$ parallel speed-up. We complement
this result with a lower bound showing this is in general the best possible. On
the other extreme, we present an algorithm that achieves the ideal factor $k$
speed-up in learning performance, with communication only logarithmic in
$1/\epsilon$.
