Mean-field game theory relies on approximating games that are intractable to model due to a very large to infinite population of players. While these kinds of games can be solved analytically via the associated system of partial derivatives, this approach is not model-free, can lead to the loss of the existence or uniqueness of solutions, and may suffer from modelling bias. To reduce the dependency between the model and the game, we introduce neural mean-field games: a combination of mean-field game theory and deep learning in the form of neural stochastic differential equations. The resulting model is data-driven, lightweight, and can learn extensive strategic interactions that are hard to capture using mean-field theory alone. In addition, the model is based on automatic differentiation, making it more robust and objective than approaches based on finite differences. We highlight the efficiency and flexibility of our approach by solving two mean-field games that vary in their complexity, observability, and the presence of noise. Lastly, we illustrate the model's robustness by simulating viral dynamics based on real-world data. Here, we demonstrate that the model's ability to learn from real-world data helps to accurately model the evolution of an epidemic outbreak. Using these results, we show that the model is flexible, generalizable, and requires few observations to learn the distribution underlying the data.

翻译：平均场博弈理论依赖于对因玩家数量极大乃至无穷而难以建模的博弈进行近似。尽管这类博弈可通过相关的偏微分方程组进行解析求解，但该方法并非无模型，可能导致解的存在性或唯一性丧失，并可能存在建模偏差。为了降低模型与博弈之间的依赖性，我们提出了神经平均场博弈：将平均场博弈理论与深度学习以神经随机微分方程的形式相结合。由此产生的模型是数据驱动的、轻量级的，并且能够学习仅靠平均场理论难以捕捉的广泛策略性互动。此外，该模型基于自动微分，使其比基于有限差分的方法更稳健、更客观。我们通过求解两个复杂程度、可观测性和噪声存在性各异的平均场博弈，突出了我们方法的效率和灵活性。最后，我们通过基于真实世界数据模拟病毒动力学，展示了该模型的稳健性。在此，我们证明了该模型从真实世界数据中学习的能力有助于准确模拟疫情爆发的演变。基于这些结果，我们表明该模型具有灵活性、可泛化性，并且只需少量观测即可学习数据背后的分布。