  We study the problem of regret minimization for distributed bandits learning,
in which $M$ agents work collaboratively to minimize their total regret under
the coordination of a central server. Our goal is to design communication
protocols with near-optimal regret and little communication cost, which is
measured by the total amount of transmitted data. For distributed multi-armed
bandits, we propose a protocol with near-optimal regret and only $O(M\log(MK))$
communication cost, where $K$ is the number of arms. The communication cost is
independent of the time horizon $T$, has only logarithmic dependence on the
number of arms, and matches the lower bound except for a logarithmic factor.
For distributed $d$-dimensional linear bandits, we propose a protocol that
achieves near-optimal regret and has communication cost of order
$\tilde{O}(Md)$, which has only logarithmic dependence on $T$.
