# Cooperative Multi-Agent Graph Bandits: UCB Algorithm and Regret Analysis

arXiv: https://arxiv.org/abs/2401.10383 · HTML: https://mlsanity.com/paper/2401.10383/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 30 references that are in the map.
- First posted on arXiv 18 Jan 2024.

## Builds on (most cited first, 11 of 11)

- [Introduction to Multi-Armed Bandits](https://mlsanity.com/paper/1904.07272/) (2019)
- [Combinatorial Multi-Armed Bandit and Its Extension to Probabilistically Triggered Arms](https://mlsanity.com/paper/1407.8339/) (2014)
- [Thompson Sampling for Combinatorial Semi-Bandits](https://mlsanity.com/paper/1803.04623/) (2018)
- [Distributed Cooperative Decision-Making in Multiarmed Bandits: Frequentist and Bayesian Algorithms](https://mlsanity.com/paper/1606.00911/) (2016)
- [Social Learning in Multi Agent Multi Armed Bandits](https://mlsanity.com/paper/1910.02100/) (2019)
- [SIC-MMAB: Synchronisation Involves Communication in Multiplayer Multi-Armed Bandits](https://mlsanity.com/paper/1809.08151/) (2018)
- [The Gossiping Insert-Eliminate Algorithm for Multi-Agent Bandits](https://mlsanity.com/paper/2001.05452/) (2020)
- [Multi-Agent Multi-Armed Bandits with Limited Communication](https://mlsanity.com/paper/2102.08462/) (2021)
- [Near-Optimal Multi-Agent Learning for Safe Coverage Control](https://mlsanity.com/paper/2210.06380/) (2022)
- [Multi-armed Bandit Learning on a Graph](https://mlsanity.com/paper/2209.09419/) (2022)
- [A Submodularity-Based Approach for Multi-Agent Optimal Coverage Problems](https://mlsanity.com/paper/1708.04201/) (2017)

## Built on by (most cited first, 1 of 1)

- [Learning from Local Walks on Dynamic Graphs with Bandit Feedback](https://mlsanity.com/paper/2607.10571/) (2026)

## Abstract (arXiv)

In this paper, we formulate the multi-agent graph bandit problem as a multi-agent extension of the graph bandit problem introduced by Zhang, Johansson, and Li [CISS 57, 1-6 (2023)]. In our formulation, N cooperative agents travel on a connected graph G with K nodes. Upon arrival at each node, agents observe a random reward drawn from a node-dependent probability distribution. The reward of the system is modeled as a weighted sum of the rewards the agents observe, where the weights capture some transformation of the reward associated with multiple agents sampling the same node at the same time. We propose an Upper Confidence Bound (UCB)-based learning algorithm, Multi-G-UCB, and prove that its expected regret over T steps is bounded by O(γ Nlog(T)[√KT + DK]), where D is the diameter of graph G and γ a boundedness parameter associated with the weight functions. Lastly, we numerically test our algorithm by comparing it to alternative methods.