In this paper, we present a deep learning framework for solving large-scale multi-agent non-cooperative stochastic games using fictitious play. The Hamilton-Jacobi-Bellman (HJB) PDE associated with each agent is reformulated into a set of Forward-Backward Stochastic Differential Equations (FBSDEs) and solved via forward sampling on a suitably defined neural network architecture. Decision-making in multi-agent systems suffers from the curse of dimensionality and strategy degeneration as the number of agents and time horizon increase. We propose a novel Deep FBSDE controller framework which is shown to outperform the current state-of-the-art deep fictitious play algorithm on a high dimensional inter-bank lending/borrowing problem. More importantly, our approach mitigates the curse of many agents and reduces computational and memory complexity, allowing us to scale up to 1,000 agents in simulation, a scale which, to the best of our knowledge, represents a new state of the art. Finally, we showcase the framework's applicability in robotics on a belief-space autonomous racing problem.

中文翻译：

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大规模随机微分对策的多主体深度FBSDE表示

在本文中，我们提出了一种深度学习框架，用于使用虚拟游戏解决大型多代理非合作随机游戏。与每个代理相关的汉密尔顿-雅各比-贝尔曼（HJB）PDE被重新公式化为一组正向-反向随机微分方程（FBSDE），并通过在适当定义的神经网络体系结构上的正向采样进行求解。随着代理数量和时间范围的增加，多代理系统中的决策会遭受维度和策略退化的诅咒。我们提出了一种新颖的Deep FBSDE控制器框架，该框架在高维银行同业拆借/借贷问题上表现出优于当前最先进的虚拟游戏算法。更重要的是，我们的方法减轻了许多代理的麻烦，并降低了计算和内存的复杂性，使我们能够在仿真中扩展多达1,000个代理，这一扩展据我们所知代表了一种最新的技术水平。最后，我们展示了该框架在信念空间自动赛车问题上在机器人技术中的适用性。