# Causal Bandits without prior knowledge using separating sets

arXiv: https://arxiv.org/abs/2009.07916 · HTML: https://mlsanity.com/paper/2009.07916/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Sep 2020.

## Built on by (most cited first, 17 of 17)

- [Designing Decision Support Systems Using Counterfactual Prediction Sets](https://mlsanity.com/paper/2306.03928/) (2023)
- [Causal Reinforcement Learning: A Survey](https://mlsanity.com/paper/2307.01452/) (2023)
- [Causal Deep Learning](https://mlsanity.com/paper/2303.02186/) (2023)
- [Causal Bandits for Linear Structural Equation Models](https://mlsanity.com/paper/2208.12764/) (2022)
- [Adaptively Exploiting d-Separators with Causal Bandits](https://mlsanity.com/paper/2202.05100/) (2022)
- [Causal Bandits without Graph Learning](https://mlsanity.com/paper/2301.11401/) (2023)
- [Additive Causal Bandits with Unknown Graph](https://mlsanity.com/paper/2306.07858/) (2023)
- [Causal Bandits with General Causal Models and Interventions](https://mlsanity.com/paper/2403.00233/) (2024)
- [Functional Causal Bayesian Optimization](https://mlsanity.com/paper/2306.06409/) (2023)
- [Linear Causal Bandits: Unknown Graph and Soft Interventions](https://mlsanity.com/paper/2411.02383/) (2024)
- [Partial Structure Discovery is Sufficient for No-regret Learning in Causal Bandits](https://mlsanity.com/paper/2411.04054/) (2024)
- [Robust Causal Bandits for Linear Models](https://mlsanity.com/paper/2310.19794/) (2023)
- [Improved Bound for Robust Causal Bandits with Linear Models](https://mlsanity.com/paper/2405.07795/) (2024)
- [Asymmetric Graph Error Control with Low Complexity in Causal Bandits](https://mlsanity.com/paper/2408.11240/) (2024)
- [Graph Agnostic Causal Bayesian Optimisation](https://mlsanity.com/paper/2411.03028/) (2024)
- [Causal Bandit Over Unknown Graphs: Upper Confidence Bounds With Backdoor Adjustment](https://mlsanity.com/paper/2502.02020/) (2025)
- [Optimal Observation-Intervention Trade-Off in Optimisation Problems with Causal Structure](https://mlsanity.com/paper/2309.02287/) (2023)

## Abstract (arXiv)

The Causal Bandit is a variant of the classic Bandit problem where an agent must identify the best action in a sequential decision-making process, where the reward distribution of the actions displays a non-trivial dependence structure that is governed by a causal model. Methods proposed for this problem thus far in the literature rely on exact prior knowledge of the full causal graph. We formulate new causal bandit algorithms that no longer necessarily rely on prior causal knowledge. Instead, they utilize an estimator based on separating sets, which we can find using simple conditional independence tests or causal discovery methods. We show that, given a true separating set, for discrete i.i.d. data, this estimator is unbiased, and has variance which is upper bounded by that of the sample mean. We develop algorithms based on Thompson Sampling and UCB for discrete and Gaussian models respectively and show increased performance on simulation data as well as on a bandit drawing from real-world protein signaling data.