Fixed-Confidence Best-Arm Identification for Causal Mediation Analysis

2026-07-05

AI Summary

This study addresses the problem of identifying the optimal intervention strategy that maximizes the Natural Direct Potential Outcome (NDPO) within a causal bandit framework, explicitly excluding indirect effects mediated through intermediate variables. To this end, it pioneers the integration of causal mediation analysis with fixed-confidence best-arm identification, formulating the task as a semi-infinite optimization problem solvable via a cutting-set method. The proposed algorithm achieves δ-correctness and asymptotic optimality within the Track-and-Stop framework by synergistically combining techniques from causal inference, semi-infinite programming, and cutting-set optimization. Empirical evaluation on the large-scale IPinYou advertising dataset demonstrates the method’s high sample efficiency and correctness with high probability, yielding significant practical performance gains.

Abstract

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).

Problem

• causal mediation analysis
• best-arm identification
• natural direct effect
• fixed-confidence
• causal bandits

Innovation

• Causal Mediation Analysis
• Best-Arm Identification
• Natural Direct Effect
• Track-and-Stop
• Semi-infinite Optimization