# The Minimal Search Space for Conditional Causal Bandits

arXiv: https://arxiv.org/abs/2502.06577 · HTML: https://mlsanity.com/paper/2502.06577/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 33 references that are in the map.
- First posted on arXiv 10 Feb 2025.

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

- [Taming the Monster: A Fast and Simple Algorithm for Contextual Bandits](https://mlsanity.com/paper/1402.0555/) (2014)
- [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)
- [Budgeted and Non-budgeted Causal Bandits](https://mlsanity.com/paper/2012.07058/) (2020)
- [Causal Bandits with Propagating Inference](https://mlsanity.com/paper/1806.02252/) (2018)
- [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)
- [A Probabilistic Calculus of Actions](https://mlsanity.com/paper/1302.6835/) (2013)
- [Safe Exploration for Optimizing Contextual Bandits](https://mlsanity.com/paper/2002.00467/) (2020)
- [Causal inference in drug discovery and development](https://mlsanity.com/paper/2209.14664/) (2022)
- [Learning Good Interventions in Causal Graphs via Covering](https://mlsanity.com/paper/2305.04638/) (2023)
- [Causal Contextual Bandits with Adaptive Context](https://mlsanity.com/paper/2405.18626/) (2024)

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

- [Graph Learning Is Suboptimal in Causal Bandits](https://mlsanity.com/paper/2510.16811/) (2025)

## Abstract (arXiv)

Causal knowledge can be used to support decision-making problems. This has been recognized in the causal bandits literature, where a causal (multi-armed) bandit is characterized by a causal graphical model and a target variable. The arms are then interventions on the causal model, and rewards are samples of the target variable. Causal bandits were originally studied with a focus on hard interventions. We focus instead on cases where the arms are conditional interventions, which more accurately model many real-world decision-making problems by allowing the value of the intervened variable to be chosen based on the observed values of other variables. This paper presents a graphical characterization of the minimal set of nodes guaranteed to contain the optimal conditional intervention, which maximizes the expected reward. We then propose an efficient algorithm with a time complexity of O(|V| + |E|) to identify this minimal set of nodes. We prove that the graphical characterization and the proposed algorithm are correct. Finally, we empirically demonstrate that our algorithm significantly prunes the search space and substantially accelerates convergence rates when integrated into standard multi-armed bandit algorithms.