Causal Graph ODE: Continuous Treatment Effect Modeling in Multi-agent
  Dynamical Systems
Zijie Huang Jeehyun Hwang Junkai Zhang Jinwoo Baik Weitong Zhang Dominik Wodarz Yizhou Sun Quanquan Gu Wei Wang
Real-world multi-agent systems are often dynamic and continuous, where the
agents co-evolve and undergo changes in their trajectories and interactions
over time. For example, the COVID-19 transmission in the U.S. can be viewed as
a multi-agent system, where states act as agents and daily population movements
between them are interactions. Estimating the counterfactual outcomes in such
systems enables accurate future predictions and effective decision-making, such
as formulating COVID-19 policies. However, existing methods fail to model the
continuous dynamic effects of treatments on the outcome, especially when
multiple treatments (e.g., "stay-at-home" and "get-vaccine" policies) are
applied simultaneously. To tackle this challenge, we propose Causal Graph
Ordinary Differential Equations (CAG-ODE), a novel model that captures the
continuous interaction among agents using a Graph Neural Network (GNN) as the
ODE function. The key innovation of our model is to learn time-dependent
representations of treatments and incorporate them into the ODE function,
enabling precise predictions of potential outcomes. To mitigate confounding
bias, we further propose two domain adversarial learning-based objectives,
which enable our model to learn balanced continuous representations that are
not affected by treatments or interference. Experiments on two datasets (i.e.,
COVID-19 and tumor growth) demonstrate the superior performance of our proposed
model.