# Confounded Budgeted Causal Bandits

arXiv: https://arxiv.org/abs/2401.07578 · HTML: https://mlsanity.com/paper/2401.07578/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 43 references that are in the map.
- First posted on arXiv 15 Jan 2024.

## Builds on (most cited first, 12 of 12)

- [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)
- [Lipschitz Bandits: Regret Lower Bounds and Optimal Algorithms](https://mlsanity.com/paper/1405.4758/) (2014)
- [Cost-Optimal Learning of Causal Graphs](https://mlsanity.com/paper/1703.02645/) (2017)
- [Budgeted and Non-budgeted Causal Bandits](https://mlsanity.com/paper/2012.07058/) (2020)
- [Experimental Design for Cost-Aware Learning of Causal Graphs](https://mlsanity.com/paper/1810.11867/) (2018)
- [Identifying Causal Effects via Context-specific Independence Relations](https://mlsanity.com/paper/2009.09768/) (2020)
- [A Causal Bandit Approach to Learning Good Atomic Interventions in Presence of Unobserved Confounders](https://mlsanity.com/paper/2107.02772/) (2021)
- [Learning Bayesian Networks in the Presence of Structural Side Information](https://mlsanity.com/paper/2112.10884/) (2021)
- [Causal Imitability Under Context-Specific Independence Relations](https://mlsanity.com/paper/2306.00585/) (2023)
- [On sample complexity of conditional independence testing with Von Mises estimator with application to causal discovery](https://mlsanity.com/paper/2310.13553/) (2023)
- [Causal Effect Identification in Uncertain Causal Networks](https://mlsanity.com/paper/2208.04627/) (2022)

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

- [Graph-Dependent Regret Bounds in Multi-Armed Bandits with Interference](https://mlsanity.com/paper/2503.07555/) (2025)
- [Graph Learning Is Suboptimal in Causal Bandits](https://mlsanity.com/paper/2510.16811/) (2025)
- [Causal Contextual Bandits with Adaptive Context](https://mlsanity.com/paper/2405.18626/) (2024)
- [Active Context Selection Improves Simple Regret in Contextual Bandits](https://mlsanity.com/paper/2605.20040/) (2026)

## Abstract (arXiv)

We study the problem of learning 'good' interventions in a stochastic environment modeled by its underlying causal graph. Good interventions refer to interventions that maximize rewards. Specifically, we consider the setting of a pre-specified budget constraint, where interventions can have non-uniform costs. We show that this problem can be formulated as maximizing the expected reward for a stochastic multi-armed bandit with side information. We propose an algorithm to minimize the cumulative regret in general causal graphs. This algorithm trades off observations and interventions based on their costs to achieve the optimal reward. This algorithm generalizes the state-of-the-art methods by allowing non-uniform costs and hidden confounders in the causal graph. Furthermore, we develop an algorithm to minimize the simple regret in the budgeted setting with non-uniform costs and also general causal graphs. We provide theoretical guarantees, including both upper and lower bounds, as well as empirical evaluations of our algorithms. Our empirical results showcase that our algorithms outperform the state of the art.