  The decentralized stochastic multi-player multi-armed bandit (MP-MAB)
problem, where the collision information is not available to the players, is
studied in this paper. Building on the seminal work of Boursier and Perchet
(2019), we propose error correction synchronization involving communication
(EC-SIC), whose regret is shown to approach that of the centralized stochastic
MP-MAB with collision information. By recognizing that the communication phase
without collision information corresponds to the Z-channel model in information
theory, the proposed EC-SIC algorithm applies optimal error correction coding
for the communication of reward statistics. A fixed message length, as opposed
to the logarithmically growing one in Boursier and Perchet (2019), also plays a
crucial role in controlling the communication loss. Experiments with practical
Z-channel codes, such as repetition code, flip code and modified Hamming code,
demonstrate the superiority of EC-SIC in both synthetic and real-world
datasets.
