On No-Sensing Adversarial Multi-player Multi-armed Bandits with Collision Communications

TL;DR

This paper introduces a new approach to adversarial multi-player multi-armed bandits by defining attackability, and develops algorithms with collision-based communication to achieve sublinear regret, addressing both attackability-aware and unaware scenarios.

Contribution

It proposes the A2C2 family of algorithms utilizing collision communication and error-correction coding, introducing a novel attackability dimension and providing theoretical regret bounds.

Findings

Asymptotic attackability-dependent sublinear regret achieved.

No exponential regret dependence on the number of players.

Effective estimation of attackability using error-detection codes.

Abstract

We study the notoriously difficult no-sensing adversarial multi-player multi-armed bandits (MP-MAB) problem from a new perspective. Instead of focusing on the hardness of multiple players, we introduce a new dimension of hardness, called attackability. All adversaries can be categorized based on the attackability and we introduce Adversary-Adaptive Collision-Communication (A2C2), a family of algorithms with forced-collision communication among players. Both attackability-aware and unaware settings are studied, and information-theoretic tools of the Z-channel model and error-correction coding are utilized to address the challenge of implicit communication without collision information in an adversarial environment. For the more challenging attackability-unaware problem, we propose a simple method to estimate the attackability enabled by a novel error-detection repetition code and randomized communication for synchronization. Theoretical analysis proves that asymptotic attackability-dependent sublinear regret can be achieved, with or without knowing the attackability. In particular, the asymptotic regret does not have an exponential dependence on the number of players, revealing a fundamental tradeoff between the two dimensions of hardness in this problem.