Estimating Causal Effects in Networks with Cluster-Based Bandits

TL;DR

This work tackles causal effect estimation under network interference, where standard A/B testing suffers from spillover. It introduces three MAB-based designs—node-based, cluster-based, and CMatch-based—to adaptively assign treatments as nodes arrive, aiming to learn the total treatment effect $\text{TTE}$ while maximizing the reward-action ratio. Empirical results on real networks with simulated interference show that cluster-based approaches achieve higher efficiency (better $\text{R/A}$) with only modest increases in $\text{TTE}$ error compared to A/B tests, and they tend to converge after observing a subset of the network. The proposed methods offer scalable, data-efficient alternatives for network experiments where interference cannot be ignored, with practical relevance for online platforms conducting causal inference in social graphs.

Abstract

The gold standard for estimating causal effects is randomized controlled trial (RCT) or A/B testing where a random group of individuals from a population of interest are given treatment and the outcome is compared to a random group of individuals from the same population. However, A/B testing is challenging in the presence of interference, commonly occurring in social networks, where individuals can impact each others outcome. Moreover, A/B testing can incur a high performance loss when one of the treatment arms has a poor performance and the test continues to treat individuals with it. Therefore, it is important to design a strategy that can adapt over time and efficiently learn the total treatment effect in the network. We introduce two cluster-based multi-armed bandit (MAB) algorithms to gradually estimate the total treatment effect in a network while maximizing the expected reward by making a tradeoff between exploration and exploitation. We compare the performance of our MAB algorithms with a vanilla MAB algorithm that ignores clusters and the corresponding RCT methods on semi-synthetic data with simulated interference. The vanilla MAB algorithm shows higher reward-action ratio at the cost of higher treatment effect error due to undesired spillover. The cluster-based MAB algorithms show higher reward-action ratio compared to their corresponding RCT methods without sacrificing much accuracy in treatment effect estimation.

Figures (2)

• Figure 1: Plot of reward-action ratio vs RMSE for different values of $\alpha(1$ for low exploration to $30$ for high exploration$)$ where true $TTE = 0.4$
• Figure 2: Plot of metrics for Cora, Citeseer, and WebKB datasets where true $TTE = 0.4$ and $\alpha = 8$