# Collaborative Multi-agent Stochastic Linear Bandits

arXiv: https://arxiv.org/abs/2205.06331 · HTML: https://mlsanity.com/paper/2205.06331/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 25 references that are in the map.
- First posted on arXiv 12 May 2022.

## Builds on (most cited first, 9 of 9)

- [Optimal algorithms for smooth and strongly convex distributed optimization in networks](https://mlsanity.com/paper/1702.08704/) (2017)
- [Bayesian Incentive-Compatible Bandit Exploration](https://mlsanity.com/paper/1502.04147/) (2015)
- [Distributed Clustering of Linear Bandits in Peer to Peer Networks](https://mlsanity.com/paper/1604.07706/) (2016)
- [Distributed Cooperative Decision-Making in Multiarmed Bandits: Frequentist and Bayesian Algorithms](https://mlsanity.com/paper/1606.00911/) (2016)
- [Distributed Cooperative Decision Making in Multi-agent Multi-armed Bandits](https://mlsanity.com/paper/2003.01312/) (2020)
- [Safe Linear Thompson Sampling with Side Information](https://mlsanity.com/paper/1911.02156/) (2019)
- [Stage-wise Conservative Linear Bandits](https://mlsanity.com/paper/2010.00081/) (2020)
- [A Dynamic Observation Strategy for Multi-agent Multi-armed Bandit Problem](https://mlsanity.com/paper/2004.03793/) (2020)
- [Distributed Detection : Finite-time Analysis and Impact of Network Topology](https://mlsanity.com/paper/1409.8606/) (2014)

## Built on by (most cited first, 4 of 4)

- [Cooperative Multi-Agent Constrained Stochastic Linear Bandits](https://mlsanity.com/paper/2410.17382/) (2024)
- [Adaptive Sample Sharing for Multi Agent Linear Bandits](https://mlsanity.com/paper/2309.08710/) (2023)
- [Distributed Optimization via Kernelized Multi-armed Bandits](https://mlsanity.com/paper/2312.04719/) (2023)
- [Multi-Agent Best Arm Identification in Stochastic Linear Bandits](https://mlsanity.com/paper/2411.13690/) (2024)

## Abstract (arXiv)

We study a collaborative multi-agent stochastic linear bandit setting, where N agents that form a network communicate locally to minimize their overall regret. In this setting, each agent has its own linear bandit problem (its own reward parameter) and the goal is to select the best global action w.r.t. the average of their reward parameters. At each round, each agent proposes an action, and one action is randomly selected and played as the network action. All the agents observe the corresponding rewards of the played actions and use an accelerated consensus procedure to compute an estimate of the average of the rewards obtained by all the agents. We propose a distributed upper confidence bound (UCB) algorithm and prove a high probability bound on its T-round regret in which we include a linear growth of regret associated with each communication round. Our regret bound is of order OBig(√fracTN log(1/|λ2|)· (log T)2Big), where λ2 is the second largest (in absolute value) eigenvalue of the communication matrix.