Meet Me at the Arm: The Cooperative Multi-Armed Bandits Problem with Shareable Arms

TL;DR

This paper introduces a decentralized algorithm for multi-player multi-armed bandits with unknown arm capacities and no collision sensing, achieving logarithmic regret.

Contribution

It presents A-CAPELLA, a novel decentralized algorithm that handles capacity-aware learning and coordination under limited feedback.

Findings

Achieves logarithmic regret in the generalized capacity-aware setting.

Handles severe feedback limitations without collision sensing.

Provides a protocol-driven coordination mechanism.

Abstract

We study the decentralized multi-player multi-armed bandits (MMAB) problem under a no-sensing setting, where each player receives only their own reward and obtains no information about collisions. Each arm has an unknown capacity, and if the number of players pulling an arm exceeds its capacity, all players involved receive zero reward. This setting generalizes the classical unit-capacity model and introduces new challenges in coordination and capacity discovery under severe feedback limitations. We propose A-CAPELLA (Algorithm for Capacity-Aware Parallel Elimination for Learning and Allocation), a decentralized learning algorithm that achieves logarithmic regret in this generalized regime via protocol-driven coordination.