Multi-Player Bandits Robust to Adversarial Collisions

TL;DR

This paper introduces RESYNC, a decentralized algorithm for multi-player bandits that remains effective against malicious attackers causing collisions, with performance degrading gracefully as attacker collisions increase.

Contribution

It presents the first robust, decentralized algorithm for defending multi-player bandits against malicious collisions, with proven optimality and agnostic to attacker strategies.

Findings

RESYNC's performance degrades as (C) with attacker collisions.

The algorithm is order-optimal, matching the lower bound scaling as (C).

RESYNC is agnostic to attacker strategies and collision counts.

Abstract

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 $\Omega(C)$. This algorithm is agnostic to the algorithm used by the attackers and agnostic to the number of collisions $C$ faced from attackers.