# A Causal Bandit Approach to Learning Good Atomic Interventions in Presence of Unobserved Confounders

arXiv: https://arxiv.org/abs/2107.02772 · HTML: https://mlsanity.com/paper/2107.02772/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 33 references that are in the map.
- First posted on arXiv 6 Jul 2021.

## Builds on (most cited first, 11 of 11)

- [Introduction to Multi-Armed Bandits](https://mlsanity.com/paper/1904.07272/) (2019)
- [Causal Bandits: Learning Good Interventions via Causal Inference](https://mlsanity.com/paper/1606.03203/) (2016)
- [Causal Networks: Semantics and Expressiveness](https://mlsanity.com/paper/1304.2379/) (2013)
- [Identifying Best Interventions through Online Importance Sampling](https://mlsanity.com/paper/1701.02789/) (2017)
- [Budgeted and Non-budgeted Causal Bandits](https://mlsanity.com/paper/2012.07058/) (2020)
- [Causal Bandits with Unknown Graph Structure](https://mlsanity.com/paper/2106.02988/) (2021)
- [Learning and Testing Causal Models with Interventions](https://mlsanity.com/paper/1805.09697/) (2018)
- [Contextual Bandits with Latent Confounders: An NMF Approach](https://mlsanity.com/paper/1606.00119/) (2016)
- [Causal Bandits with Propagating Inference](https://mlsanity.com/paper/1806.02252/) (2018)
- [Causal Markov Decision Processes: Learning Good Interventions Efficiently](https://mlsanity.com/paper/2102.07663/) (2021)
- [Learning and Sampling of Atomic Interventions from Observations](https://mlsanity.com/paper/2002.04232/) (2020)

## Built on by (most cited first, 15 of 15)

- [Causal Deep Learning](https://mlsanity.com/paper/2303.02186/) (2023)
- [Causal Bandits for Linear Structural Equation Models](https://mlsanity.com/paper/2208.12764/) (2022)
- [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)
- [Learning Good Interventions in Causal Graphs via Covering](https://mlsanity.com/paper/2305.04638/) (2023)
- [Linear Causal Bandits: Unknown Graph and Soft Interventions](https://mlsanity.com/paper/2411.02383/) (2024)
- [Robust Causal Bandits for Linear Models](https://mlsanity.com/paper/2310.19794/) (2023)
- [Confounded Budgeted Causal Bandits](https://mlsanity.com/paper/2401.07578/) (2024)
- [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)
- [Causal Contextual Bandits with Adaptive Context](https://mlsanity.com/paper/2405.18626/) (2024)
- [Causal Bandit Over Unknown Graphs: Upper Confidence Bounds With Backdoor Adjustment](https://mlsanity.com/paper/2502.02020/) (2025)
- [The Minimal Search Space for Conditional Causal Bandits](https://mlsanity.com/paper/2502.06577/) (2025)
- [Generator-Mediated Bandits: Thompson Sampling for GenAI-Powered Adaptive Interventions](https://mlsanity.com/paper/2505.16311/) (2025)
- [Active Context Selection Improves Simple Regret in Contextual Bandits](https://mlsanity.com/paper/2605.20040/) (2026)

## Abstract (arXiv)

We study the problem of determining the best intervention in a Causal Bayesian Network (CBN) specified only by its causal graph. We model this as a stochastic multi-armed bandit (MAB) problem with side-information, where the interventions correspond to the arms of the bandit instance. First, we propose a simple regret minimization algorithm that takes as input a semi-Markovian causal graph with atomic interventions and possibly unobservable variables, and achieves tildeO(√M/T) expected simple regret, where M is dependent on the input CBN and could be very small compared to the number of arms. We also show that this is almost optimal for CBNs described by causal graphs having an n-ary tree structure. Our simple regret minimization results, both upper and lower bound, subsume previous results in the literature, which assumed additional structural restrictions on the input causal graph. In particular, our results indicate that the simple regret guarantee of our proposed algorithm can only be improved by considering more nuanced structural restrictions on the causal graph. Next, we propose a cumulative regret minimization algorithm that takes as input a general causal graph with all observable nodes and atomic interventions and performs better than the optimal MAB algorithm that does not take causal side-information into account. We also experimentally compare both our algorithms with the best known algorithms in the literature. To the best of our knowledge, this work gives the first simple and cumulative regret minimization algorithms for CBNs with general causal graphs under atomic interventions and having unobserved confounders.