Multi-agent dynamical systems refer to scenarios where multiple units interact with each other and evolve collectively over time. To make informed decisions in multi-agent dynamical systems, such as determining the optimal vaccine distribution plan, it is essential for decision-makers to estimate the continuous-time counterfactual outcomes. However, existing studies of causal inference over time rely on the assumption that units are mutually independent, which is not valid for multi-agent dynamical systems. In this paper, we aim to bridge this gap and study how to estimate counterfactual outcomes in multi-agent dynamical systems. Causal inference in a multi-agent dynamical system has unique challenges: 1) Confounders are time-varying and are present in both individual unit covariates and those of other units; 2) Units are affected by not only their own but also others' treatments; 3) The treatments are naturally dynamic, such as receiving vaccines and boosters in a seasonal manner. We model a multi-agent dynamical system as a graph and propose CounterFactual GraphODE (CF-GODE), a causal model that estimates continuous-time counterfactual outcomes in the presence of inter-dependencies between units. To facilitate continuous-time estimation, we propose Treatment-Induced GraphODE, a novel ordinary differential equation based on GNN, which incorporates dynamical treatments as additional inputs to predict potential outcomes over time. To remove confounding bias, we propose two domain adversarial learning based objectives that learn balanced continuous representation trajectories, which are not predictive of treatments and interference. We further provide theoretical justification to prove their effectiveness. Experiments on two semi-synthetic datasets confirm that CF-GODE outperforms baselines on counterfactual estimation. We also provide extensive analyses to understand how our model works.

翻译：多智能体动力系统是指多个单元相互交互并随时间共同演化的场景。为了在多智能体动力系统中制定明智的决策（例如确定最佳疫苗分配方案），决策者需要估计连续时间的反事实结果。然而，现有的随时间演化的因果推断研究依赖于单元间相互独立的假设，而这在多智能体动力系统中并不成立。本文旨在弥合这一差距，研究如何估计多智能体动力系统中的反事实结果。多智能体动力系统中的因果推断面临独特挑战：1) 混淆变量随时间变化，且同时存在于个体单元协变量和其他单元协变量中；2) 单元不仅受自身处理影响，也受其他单元处理影响；3) 处理本身具有动态性，例如季节性接种疫苗和加强针。我们将多智能体动力系统建模为图，并提出反事实图神经ODE（CounterFactual GraphODE，简称CF-GODE），这是一种考虑单元间相互依赖关系的因果模型，用于估计连续时间的反事实结果。为实现连续时间估计，我们提出基于图神经网络的新型常微分方程——处理诱导图神经ODE（Treatment-Induced GraphODE），该方程将动态处理作为额外输入，以预测随时间演化的潜在结果。为消除混淆偏差，我们提出两个基于领域对抗学习的目标函数，通过学习平衡的连续表示轨迹（这些轨迹与处理及干扰无关）来消除偏差。我们进一步提供理论证明以验证其有效性。在两个半合成数据集上的实验证实，CF-GODE在反事实估计上优于基线方法。我们还进行了广泛分析以理解模型的工作机制。