  Multi-armed bandits (MAB) is a sequential decision-making model in which the
learner controls the trade-off between exploration and exploitation to maximize
its cumulative reward. Federated multi-armed bandits (FMAB) is an emerging
framework where a cohort of learners with heterogeneous local models play an
MAB game and communicate their aggregated feedback to a server to learn a
globally optimal arm. Two key hurdles in FMAB are communication-efficient
learning and resilience to adversarial attacks. To address these issues, we
study the FMAB problem in the presence of Byzantine clients who can send false
model updates threatening the learning process. We analyze the sample
complexity and the regret of $\beta$-optimal arm identification. We borrow
tools from robust statistics and propose a median-of-means (MoM)-based online
algorithm, Fed-MoM-UCB, to cope with Byzantine clients. In particular, we show
that if the Byzantine clients constitute less than half of the cohort, the
cumulative regret with respect to $\beta$-optimal arms is bounded over time
with high probability, showcasing both communication efficiency and Byzantine
resilience. We analyze the interplay between the algorithm parameters, a
discernibility margin, regret, communication cost, and the arms' suboptimality
gaps. We demonstrate Fed-MoM-UCB's effectiveness against the baselines in the
presence of Byzantine attacks via experiments.
