  Multi-player multi-armed bandit is an increasingly relevant decision-making
problem, motivated by applications to cognitive radio systems. Most research
for this problem focuses exclusively on the settings that players have
\textit{full access} to all arms and receive no reward when pulling the same
arm. Hence all players solve the same bandit problem with the goal of
maximizing their cumulative reward. However, these settings neglect several
important factors in many real-world applications, where players have
\textit{limited access} to \textit{a dynamic local subset of arms} (i.e., an
arm could sometimes be ``walking'' and not accessible to the player). To this
end, this paper proposes a \textit{multi-player multi-armed walking bandits}
model, aiming to address aforementioned modeling issues. The goal now is to
maximize the reward, however, players can only pull arms from the local subset
and only collect a full reward if no other players pull the same arm. We adopt
Upper Confidence Bound (UCB) to deal with the exploration-exploitation tradeoff
and employ distributed optimization techniques to properly handle collisions.
By carefully integrating these two techniques, we propose a decentralized
algorithm with near-optimal guarantee on the regret, and can be easily
implemented to obtain competitive empirical performance.
