  We study the problem of best-arm identification in a distributed variant of
the multi-armed bandit setting, with a central learner and multiple agents.
Each agent is associated with an arm of the bandit, generating stochastic
rewards following an unknown distribution. Further, each agent can communicate
the observed rewards with the learner over a bit-constrained channel. We
propose a novel quantization scheme called Inflating Confidence for
Quantization (ICQ) that can be applied to existing confidence-bound based
learning algorithms such as Successive Elimination. We analyze the performance
of ICQ applied to Successive Elimination and show that the overall algorithm,
named ICQ-SE, has the order-optimal sample complexity as that of the
(unquantized) SE algorithm. Moreover, it requires only an exponentially sparse
frequency of communication between the learner and the agents, thus requiring
considerably fewer bits than existing quantization schemes to successfully
identify the best arm. We validate the performance improvement offered by ICQ
with other quantization methods through numerical experiments.
