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.

本文研究了多智能体动态系统中的因果推断问题，提出了 CounterFactual GraphODE 的模型，以解决因果推断中的互依性问题，并用于预测连续时间的反事实结果。

CF-GODE: 多智能体动态系统连续时间因果推断

CF-GODE: Continuous-Time Causal Inference for Multi-Agent Dynamical  Systems

We propose an approach to modelling large-scale multi-agent dynamical systems
allowing interactions among more than just pairs of agents using the theory of
mean field games and the notion of hypergraphons, which are obtained as limits
of large hypergraphs. To the best of our knowledge, ours is the first work on
mean field games on hypergraphs. Together with an extension to a multi-layer
setup, we obtain limiting descriptions for large systems of non-linear,
weakly-interacting dynamical agents. On the theoretical side, we prove the
well-foundedness of the resulting hypergraphon mean field game, showing both
existence and approximate Nash properties. On the applied side, we extend
numerical and learning algorithms to compute the hypergraphon mean field
equilibria. To verify our approach empirically, we consider a social rumor
spreading model, where we give agents intrinsic motivation to spread rumors to
unaware agents, and an epidemics control problem.

使用超图的概念和均值场博弈理论，提出了一种建模大规模多智能体动力系统的方法，可以跨超过两个 Agent 进行交互，该方法被扩展到多层设置中，并被用于社交舆论和传染病控制问题的实证研究。