Heterogeneous Multi-Player Multi-Armed Bandits Robust To Adversarial Attacks

TL;DR

This paper studies a multi-player multi-armed bandit problem with heterogeneous rewards and adversarial attacks, proposing a communication-based policy that achieves near-optimal regret despite adversarial interference.

Contribution

It introduces a new policy allowing players to communicate briefly, effectively mitigating adversarial attacks in a heterogeneous multi-player bandit setting.

Findings

Achieves near order optimal regret of O(log^{1+δ} T + W)

Handles multiple adversarial attacks per time step

Supports heterogeneous reward distributions across players

Abstract

We consider a multi-player multi-armed bandit setting in the presence of adversaries that attempt to negatively affect the rewards received by the players in the system. The reward distributions for any given arm are heterogeneous across the players. In the event of a collision (more than one player choosing the same arm), all the colliding users receive zero rewards. The adversaries use collisions to affect the rewards received by the players, i.e., if an adversary attacks an arm, any player choosing that arm will receive zero reward. At any time step, the adversaries may attack more than one arm. It is assumed that the players in the system do not deviate from a pre-determined policy used by all the players, and that the probability that none of the arms face adversarial attacks is strictly positive at every time step. In order to combat the adversarial attacks, the players are allowed to communicate using a single bit for $O(\log T)$ time units, where $T$ is the time horizon, and each player can only observe their own actions and rewards at all time steps. We propose a {policy that is used by all the players, which} achieves near order optimal regret of order $O(\log^{1+\delta}T + W)$, where $W$ is total number of time units for which there was an adversarial attack on at least one arm.