# Fixed-Confidence Best-Arm Identification for Causal Mediation Analysis

arXiv: https://arxiv.org/abs/2607.04315 · HTML: https://mlsanity.com/paper/2607.04315/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 28 references that are in the map.
- First posted on arXiv 5 Jul 2026.

## Builds on (most cited first, 7 of 7)

- [On the Complexity of Best Arm Identification in Multi-Armed Bandit Models](https://mlsanity.com/paper/1407.4443/) (2014)
- [Direct and Indirect Effects](https://mlsanity.com/paper/1301.2300/) (2013)
- [Optimal Best Arm Identification with Fixed Confidence](https://mlsanity.com/paper/1602.04589/) (2016)
- [Simple Bayesian Algorithms for Best Arm Identification](https://mlsanity.com/paper/1602.08448/) (2016)
- [Causal Bandits: Learning Good Interventions via Causal Inference](https://mlsanity.com/paper/1606.03203/) (2016)
- [Real-Time Bidding Benchmarking with iPinYou Dataset](https://mlsanity.com/paper/1407.7073/) (2014)
- [A Potential Outcomes Calculus for Identifying Conditional Path-Specific Effects](https://mlsanity.com/paper/1903.03662/) (2019)

## Abstract (arXiv)

This paper studies the problem of identifying the treatment that maximizes the expected natural direct potential outcome (NDPO), which captures the potential outcome of an intervention while excluding the pathway transmitted through a mediator that researchers may wish to remove from evaluation. We first establish population-level identification of the expected NDPO in a causal bandit setting using observable interventional distributions. We then develop a fixed-confidence best-arm identification (BAI) algorithm based on the Track-and-Stop (TaS) framework, employing a cutting-set method to solve the resulting semi-infinite optimization problem. The proposed algorithm achieves sample-efficient identification with a high-probability correctness guarantee. We prove that it satisfies δ-correctness and asymptotic optimality. Finally, we validate the approach through empirical evaluations on a large-scale real-world advertising dataset (IPinYou).