# Causal Bandit Over Unknown Graphs: Upper Confidence Bounds With Backdoor Adjustment

arXiv: https://arxiv.org/abs/2502.02020 · HTML: https://mlsanity.com/paper/2502.02020/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 33 references that are in the map.
- First posted on arXiv 4 Feb 2025.

## Builds on (most cited first, 13 of 13)

- [Learning to Optimize Via Posterior Sampling](https://mlsanity.com/paper/1301.2609/) (2013)
- [Multi-armed Bandit Models for the Optimal Design of Clinical Trials: Benefits and Challenges](https://mlsanity.com/paper/1507.08025/) (2015)
- [Causal Bandits: Learning Good Interventions via Causal Inference](https://mlsanity.com/paper/1606.03203/) (2016)
- [Identifying Best Interventions through Online Importance Sampling](https://mlsanity.com/paper/1701.02789/) (2017)
- [Nested Markov Properties for Acyclic Directed Mixed Graphs](https://mlsanity.com/paper/1701.06686/) (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)
- [Causal Bandits with Propagating Inference](https://mlsanity.com/paper/1806.02252/) (2018)
- [Causal Bandits for Linear Structural Equation Models](https://mlsanity.com/paper/2208.12764/) (2022)
- [Causal Bandits without prior knowledge using separating sets](https://mlsanity.com/paper/2009.07916/) (2020)
- [A Causal Bandit Approach to Learning Good Atomic Interventions in Presence of Unobserved Confounders](https://mlsanity.com/paper/2107.02772/) (2021)
- [Causal Bandits without Graph Learning](https://mlsanity.com/paper/2301.11401/) (2023)
- [Linear Causal Bandits: Unknown Graph and Soft Interventions](https://mlsanity.com/paper/2411.02383/) (2024)

## Built on by (most cited first, 1 of 1)

- [Mathematical Reasoning via Intervention-Based Time-Series Causal Discovery Using LLMs as Concept Mastery Simulators](https://mlsanity.com/paper/2605.07600/) (2026)

## Abstract (arXiv)

The causal bandit problem seeks to identify, through sequential experimentation, an intervention that maximizes the expected reward in a causal system modeled by a directed acyclic graph (DAG). Existing methods typically assume that the causal graph is known or impose restrictive structural assumptions. In this paper, we study causal bandit problems when the causal graph is unknown. We first consider Gaussian DAG models without latent confounders. By combining observational and experimental data collected sequentially during the bandit process, we identify candidate backdoor adjustment sets for each intervention arm. These sets enable estimation of causal effects and construction of upper confidence bounds that integrate information from both data sources. Based on these estimates, we propose a new algorithm, termed backdoor-adjustment upper confidence bound (BA-UCB), for sequential intervention selection. We establish finite-time upper bounds on the cumulative regret of BA-UCB, showing improved rates and substantially relaxed dependency on the number of intervention arms compared to standard multi-armed bandit methods. We further extend the methodology and theoretical guarantees to settings with latent confounders, where the observed variables are modeled by an acyclic directed mixed graph. Simulation studies demonstrate that BA-UCB achieves substantially lower cumulative regret and favorable computational efficiency relative to existing approaches.