# Learning in Distributed Contextual Linear Bandits Without Sharing the Context

arXiv: https://arxiv.org/abs/2206.04180 · HTML: https://mlsanity.com/paper/2206.04180/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 41 references that are in the map.
- First posted on arXiv 8 Jun 2022.

## Builds on (most cited first, 14 of 14)

- [QSGD: Communication-Efficient SGD via Gradient Quantization and Encoding](https://mlsanity.com/paper/1610.02132/) (2016)
- [Sequential Batch Learning in Finite-Action Linear Contextual Bandits](https://mlsanity.com/paper/2004.06321/) (2020)
- [Federated Multi-Armed Bandits](https://mlsanity.com/paper/2101.12204/) (2021)
- [A Refined Laser Method and Faster Matrix Multiplication](https://mlsanity.com/paper/2010.05846/) (2020)
- [Locally Differentially Private (Contextual) Bandits Learning](https://mlsanity.com/paper/2006.00701/) (2020)
- [Provably Optimal Algorithms for Generalized Linear Contextual Bandits](https://mlsanity.com/paper/1703.00048/) (2017)
- [An Efficient Algorithm For Generalized Linear Bandit: Online Stochastic Gradient Descent and Thompson Sampling](https://mlsanity.com/paper/2006.04012/) (2020)
- [Dynamic Batch Learning in High-Dimensional Sparse Linear Contextual Bandits](https://mlsanity.com/paper/2008.11918/) (2020)
- [RATQ: A Universal Fixed-Length Quantizer for Stochastic Optimization](https://mlsanity.com/paper/1908.08200/) (2019)
- [Solving Multi-Arm Bandit Using a Few Bits of Communication](https://mlsanity.com/paper/2111.06067/) (2021)
- [On Distributed Quantization for Classification](https://mlsanity.com/paper/1911.00216/) (2019)
- [Bandit Models of Human Behavior: Reward Processing in Mental Disorders](https://mlsanity.com/paper/1706.02897/) (2017)
- [Quantizing data for distributed learning](https://mlsanity.com/paper/2012.07913/) (2020)
- [Contextual Bandit Applications in Customer Support Bot](https://mlsanity.com/paper/2112.03210/) (2021)

## Abstract (arXiv)

Contextual linear bandits is a rich and theoretically important model that has many practical applications. Recently, this setup gained a lot of interest in applications over wireless where communication constraints can be a performance bottleneck, especially when the contexts come from a large d-dimensional space. In this paper, we consider a distributed memoryless contextual linear bandit learning problem, where the agents who observe the contexts and take actions are geographically separated from the learner who performs the learning while not seeing the contexts. We assume that contexts are generated from a distribution and propose a method that uses ≈ 5d bits per context for the case of unknown context distribution and 0 bits per context if the context distribution is known, while achieving nearly the same regret bound as if the contexts were directly observable. The former bound improves upon existing bounds by a log(T) factor, where T is the length of the horizon, while the latter achieves information theoretical tightness.