# Budgeted and Non-budgeted Causal Bandits

arXiv: https://arxiv.org/abs/2012.07058 · HTML: https://mlsanity.com/paper/2012.07058/

## Key facts

- Cited by 38 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Dec 2020.

## Built on by (most cited first, 30 of 38)

- [Causal Structure Learning: a Combinatorial Perspective](https://mlsanity.com/paper/2206.01152/) (2022)
- [A Survey on Causal Reinforcement Learning](https://mlsanity.com/paper/2302.05209/) (2023)
- [Causal Bandits with Unknown Graph Structure](https://mlsanity.com/paper/2106.02988/) (2021)
- [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)
- [Combinatorial Causal Bandits](https://mlsanity.com/paper/2206.01995/) (2022)
- [A Causal Bandit Approach to Learning Good Atomic Interventions in Presence of Unobserved Confounders](https://mlsanity.com/paper/2107.02772/) (2021)
- [Bandit Algorithms for Precision Medicine](https://mlsanity.com/paper/2108.04782/) (2021)
- [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)
- [Combinatorial Pure Exploration of Causal Bandits](https://mlsanity.com/paper/2206.07883/) (2022)
- [Causal Markov Decision Processes: Learning Good Interventions Efficiently](https://mlsanity.com/paper/2102.07663/) (2021)
- [Sample Constrained Treatment Effect Estimation](https://mlsanity.com/paper/2210.06594/) (2022)
- [Combinatorial Causal Bandits without Graph Skeleton](https://mlsanity.com/paper/2301.13392/) (2023)
- [Causal Bandits with General Causal Models and Interventions](https://mlsanity.com/paper/2403.00233/) (2024)
- [Causally Abstracted Multi-armed Bandits](https://mlsanity.com/paper/2404.17493/) (2024)
- [Learning Good Interventions in Causal Graphs via Covering](https://mlsanity.com/paper/2305.04638/) (2023)
- [Functional Causal Bayesian Optimization](https://mlsanity.com/paper/2306.06409/) (2023)
- [Exploiting Causal Graph Priors with Posterior Sampling for Reinforcement Learning](https://mlsanity.com/paper/2310.07518/) (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)
- [Confounded Budgeted Causal Bandits](https://mlsanity.com/paper/2401.07578/) (2024)
- [Uplifting Bandits](https://mlsanity.com/paper/2206.04091/) (2022)
- [Improved Bound for Robust Causal Bandits with Linear Models](https://mlsanity.com/paper/2405.07795/) (2024)
- [Causal Bandits: The Pareto Optimal Frontier of Adaptivity, a Reduction to Linear Bandits, and Limitations around Unknown Marginals](https://mlsanity.com/paper/2407.00950/) (2024)
- [Asymmetric Graph Error Control with Low Complexity in Causal Bandits](https://mlsanity.com/paper/2408.11240/) (2024)
- [Graph Learning Is Suboptimal in Causal Bandits](https://mlsanity.com/paper/2510.16811/) (2025)

## Abstract (arXiv)

Learning good interventions in a causal graph can be modelled as a stochastic multi-armed bandit problem with side-information. First, we study this problem when interventions are more expensive than observations and a budget is specified. If there are no backdoor paths from an intervenable node to the reward node then we propose an algorithm to minimize simple regret that optimally trades-off observations and interventions based on the cost of intervention. We also propose an algorithm that accounts for the cost of interventions, utilizes causal side-information, and minimizes the expected cumulative regret without exceeding the budget. Our cumulative-regret minimization algorithm performs better than standard algorithms that do not take side-information into account. Finally, we study the problem of learning best interventions without budget constraint in general graphs and give an algorithm that achieves constant expected cumulative regret in terms of the instance parameters when the parent distribution of the reward variable for each intervention is known. Our results are experimentally validated and compared to the best-known bounds in the current literature.