  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.
