# Combinatorial Causal Bandits

arXiv: https://arxiv.org/abs/2206.01995 · HTML: https://mlsanity.com/paper/2206.01995/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 39 references that are in the map.
- First posted on arXiv 4 Jun 2022.

## Builds on (most cited first, 9 of 9)

- [Causal Bandits: Learning Good Interventions via Causal Inference](https://mlsanity.com/paper/1606.03203/) (2016)
- [Combinatorial Multi-Armed Bandit and Its Extension to Probabilistically Triggered Arms](https://mlsanity.com/paper/1407.8339/) (2014)
- [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)
- [Causal Bandits with Propagating Inference](https://mlsanity.com/paper/1806.02252/) (2018)
- [Online Influence Maximization under Linear Threshold Model](https://mlsanity.com/paper/2011.06378/) (2020)
- [Assumption-lean inference for generalised linear model parameters](https://mlsanity.com/paper/2006.08402/) (2020)
- [Matrix anti-concentration inequalities with applications](https://mlsanity.com/paper/2111.05553/) (2021)

## Built on by (most cited first, 16 of 16)

- [Causal Bandits for Linear Structural Equation Models](https://mlsanity.com/paper/2208.12764/) (2022)
- [Combinatorial Pure Exploration of Causal Bandits](https://mlsanity.com/paper/2206.07883/) (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)
- [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)
- [Reinforcement Learning in the Real World: A Survey of Statistical Challenges and Future Directions](https://mlsanity.com/paper/2601.15353/) (2026)
- [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)
- [Graph Learning Is Suboptimal in Causal Bandits](https://mlsanity.com/paper/2510.16811/) (2025)
- [A Correction of Pseudo Log-Likelihood Method](https://mlsanity.com/paper/2403.18127/) (2024)
- [Causal Contextual Bandits with Adaptive Context](https://mlsanity.com/paper/2405.18626/) (2024)
- [The Minimal Search Space for Conditional Causal Bandits](https://mlsanity.com/paper/2502.06577/) (2025)
- [On Transportability for Structural Causal Bandits](https://mlsanity.com/paper/2511.17953/) (2025)
- [Graph Structured Combinatorial Semi-Bandit with Nonlinear Reward Associations through Separable Signals](https://mlsanity.com/paper/2606.14650/) (2026)

## Abstract (arXiv)

In combinatorial causal bandits (CCB), the learning agent chooses at most K variables in each round to intervene, collects feedback from the observed variables, with the goal of minimizing expected regret on the target variable Y. We study under the context of binary generalized linear models (BGLMs) with a succinct parametric representation of the causal models. We present the algorithm BGLM-OFU for Markovian BGLMs (i.e. no hidden variables) based on the maximum likelihood estimation method, and show that it achieves O(√Tlog T) regret, where T is the time horizon. For the special case of linear models with hidden variables, we apply causal inference techniques such as the do-calculus to convert the original model into a Markovian model, and then show that our BGLM-OFU algorithm and another algorithm based on the linear regression both solve such linear models with hidden variables. Our novelty includes (a) considering the combinatorial intervention action space and the general causal models including ones with hidden variables, (b) integrating and adapting techniques from diverse studies such as generalized linear bandits and online influence maximization, and (c) avoiding unrealistic assumptions (such as knowing the joint distribution of the parents of Y under all interventions) and regret factors exponential to causal graph size in prior studies.