Decentralized Multi-player Multi-armed Bandits with No Collision Information
This work addresses a key limitation in decentralized bandit algorithms for scenarios like wireless networks where collision information is unavailable, representing an incremental improvement over prior methods.
The paper tackles the decentralized multi-player multi-armed bandit problem without collision information by proposing the EC-SIC algorithm, which uses error correction coding to approach the regret of centralized methods with collision information, as demonstrated in experiments with synthetic and real-world datasets.
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.