Deep Neural Networks

Abstract The simultaneous application of multiple treatments is increasingly common in many fields, such as healthcare and marketing. In such scenarios, it is important to estimate not only the effect of each single treatment effect, but also the synergistic treatment effects that arise from combinations of treatments. Previous studies have proposed methods that combine a variational autoencoder with a task embedding network, which captures treatment similarities for multi-treatment causal inference. These methods assume the presence of unobserved covariates and regard observed data as proxies for those unobserved covariates. As a result, they may still learn unnecessary latent variables even when the covariates are observed. This model misspecification can lead to misleading estimates of causal effects. To address this issue, we propose a novel deep learning framework that simultaneously captures both single and synergistic treatment effects and mitigates selection bias, using a task embedding network and a representation learning network with the balancing penalty. The task embedding network ensures that similar treatments yield similar representations and outcomes, improving the estimation of both single and synergistic effects. The representation learning network with the balancing penalty directly learns representations from observed covariates and controls distributional differences across treatment patterns using Integral Probability Metrics, thereby reducing the risk of model misspecification due to erroneous latent structures. We evaluate our method using multiple simulation datasets and compare its performance with existing baselines. Our method consistently outperforms baselines by reducing estimation errors in both single and synergistic treatment effects across settings.

Aug 4, 2025