Multi-Armed Bandits with Interference
Su Jia Peter Frazier Nathan Kallus
Experimentation with interference poses a significant challenge in
contemporary online platforms. Prior research on experimentation with
interference has concentrated on the final output of a policy. The cumulative
performance, while equally crucial, is less well understood. To address this
gap, we introduce the problem of {\em Multi-armed Bandits with Interference}
(MABI), where the learner assigns an arm to each of $N$ experimental units over
a time horizon of $T$ rounds. The reward of each unit in each round depends on
the treatments of {\em all} units, where the influence of a unit decays in the
spatial distance between units. Furthermore, we employ a general setup wherein
the reward functions are chosen by an adversary and may vary arbitrarily across
rounds and units. We first show that switchback policies achieve an optimal
{\em expected} regret $\tilde O(\sqrt T)$ against the best fixed-arm policy.
Nonetheless, the regret (as a random variable) for any switchback policy
suffers a high variance, as it does not account for $N$. We propose a cluster
randomization policy whose regret (i) is optimal in {\em expectation} and (ii)
admits a high probability bound that vanishes in $N$.