# Multi-Agent Low-Dimensional Linear Bandits

arXiv: https://arxiv.org/abs/2007.01442 · HTML: https://mlsanity.com/paper/2007.01442/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Jul 2020.

## Built on by (most cited first, 8 of 8)

- [Exploiting Heterogeneity in Robust Federated Best-Arm Identification](https://mlsanity.com/paper/2109.05700/) (2021)
- [Linear Stochastic Bandits over a Bit-Constrained Channel](https://mlsanity.com/paper/2203.01198/) (2022)
- [Distributed Linear Bandits under Communication Constraints](https://mlsanity.com/paper/2211.02212/) (2022)
- [Collaborative Linear Bandits with Adversarial Agents: Near-Optimal Regret Bounds](https://mlsanity.com/paper/2206.02834/) (2022)
- [Collaborative Multi-Agent Heterogeneous Multi-Armed Bandits](https://mlsanity.com/paper/2305.18784/) (2023)
- [Cooperative Thresholded Lasso for Sparse Linear Bandit](https://mlsanity.com/paper/2305.19161/) (2023)
- [Multi-Agent Best Arm Identification in Stochastic Linear Bandits](https://mlsanity.com/paper/2411.13690/) (2024)
- [Multi-Agent Combinatorial-Multi-Armed-Bandit framework for the Submodular Welfare Problem under Bandit Feedback](https://mlsanity.com/paper/2602.16183/) (2026)

## Abstract (arXiv)

We study a multi-agent stochastic linear bandit with side information, parameterized by an unknown vector θ^* ∈ ℝd. The side information consists of a finite collection of low-dimensional subspaces, one of which contains θ^*. In our setting, agents can collaborate to reduce regret by sending recommendations across a communication graph connecting them. We present a novel decentralized algorithm, where agents communicate subspace indices with each other and each agent plays a projected variant of LinUCB on the corresponding (low-dimensional) subspace. By distributing the search for the optimal subspace across users and learning of the unknown vector by each agent in the corresponding low-dimensional subspace, we show that the per-agent finite-time regret is much smaller than the case when agents do not communicate. We finally complement these results through simulations.