Multi-Player Bandits Robust to Adversarial Collisions
This addresses security and robustness issues in applications like cognitive radios, representing a novel extension rather than an incremental improvement.
The paper tackles the problem of malicious players obstructing cooperative players in stochastic multi-player multi-armed bandits by introducing RESYNC, a decentralized and robust algorithm that achieves performance scaling as O(C) with collisions, which is proven to be order-optimal.
Motivated by cognitive radios, stochastic Multi-Player Multi-Armed Bandits has been extensively studied in recent years. In this setting, each player pulls an arm, and receives a reward corresponding to the arm if there is no collision, namely the arm was selected by one single player. Otherwise, the player receives no reward if collision occurs. In this paper, we consider the presence of malicious players (or attackers) who obstruct the cooperative players (or defenders) from maximizing their rewards, by deliberately colliding with them. We provide the first decentralized and robust algorithm RESYNC for defenders whose performance deteriorates gracefully as $\tilde{O}(C)$ as the number of collisions $C$ from the attackers increases. We show that this algorithm is order-optimal by proving a lower bound which scales as $Ω(C)$. This algorithm is agnostic to the algorithm used by the attackers and agnostic to the number of collisions $C$ faced from attackers.