  We consider the stochastic bandit problem in the sublinear space setting,
where one cannot record the win-loss record for all $K$ arms. We give an
algorithm using $O(1)$ words of space with regret \[
  \sum_{i=1}^{K}\frac{1}{\Delta_i}\log \frac{\Delta_i}{\Delta}\log T \] where
$\Delta_i$ is the gap between the best arm and arm $i$ and $\Delta$ is the gap
between the best and the second-best arms. If the rewards are bounded away from
$0$ and $1$, this is within an $O(\log 1/\Delta)$ factor of the optimum regret
possible without space constraints.
