# Adversarial Linear Contextual Bandits with Graph-Structured Side Observations

arXiv: https://arxiv.org/abs/2012.05756 · HTML: https://mlsanity.com/paper/2012.05756/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Dec 2020.

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

- [Practical Contextual Bandits with Feedback Graphs](https://mlsanity.com/paper/2302.08631/) (2023)
- [Efficient Contextual Bandits with Uninformed Feedback Graphs](https://mlsanity.com/paper/2402.08127/) (2024)
- [Stochastic Graph Bandit Learning with Side-Observations](https://mlsanity.com/paper/2308.15107/) (2023)
- [Asymptotically-Optimal Gaussian Bandits with Side Observations](https://mlsanity.com/paper/2505.10698/) (2025)

## Abstract (arXiv)

This paper studies the adversarial graphical contextual bandits, a variant of adversarial multi-armed bandits that leverage two categories of the most common side information: contexts and side observations. In this setting, a learning agent repeatedly chooses from a set of K actions after being presented with a d-dimensional context vector. The agent not only incurs and observes the loss of the chosen action, but also observes the losses of its neighboring actions in the observation structures, which are encoded as a series of feedback graphs. This setting models a variety of applications in social networks, where both contexts and graph-structured side observations are available. Two efficient algorithms are developed based on textttEXP3. Under mild conditions, our analysis shows that for undirected feedback graphs the first algorithm, textttEXP3-LGC-U, achieves the regret of order O(√(K+α(G)d)TlogK) over the time horizon T, where α(G) is the average independence number of the feedback graphs. A slightly weaker result is presented for the directed graph setting as well. The second algorithm, textttEXP3-LGC-IX, is developed for a special class of problems, for which the regret is reduced to O(√α(G)dTlogKlog(KT)) for both directed as well as undirected feedback graphs. Numerical tests corroborate the efficiency of proposed algorithms.