  In many platforms, user arrivals exhibit a self-reinforcing behavior: future
user arrivals are likely to have preferences similar to users who were
satisfied in the past. In other words, arrivals exhibit positive externalities.
We study multiarmed bandit (MAB) problems with positive externalities. We show
that the self-reinforcing preferences may lead standard benchmark algorithms
such as UCB to exhibit linear regret. We develop a new algorithm, Balanced
Exploration (BE), which explores arms carefully to avoid suboptimal convergence
of arrivals before sufficient evidence is gathered. We also introduce an
adaptive variant of BE which successively eliminates suboptimal arms. We
analyze their asymptotic regret, and establish optimality by showing that no
algorithm can perform better.
