提出新型神经网络架构NTM，高效求解图结构多智能体博弈的纳什均衡。
Finite-Agent Stochastic Differential Games on Large Graphs: II. Graph-Based Architectures
- NTM通过图结构引导稀疏化，在前馈网络中嵌入固定非训练组件。
- 在三种图结构博弈上，性能接近全训练模型，参数量大幅减少。
- 适合金融、机器人等大规模图结构多智能体系统建模与求解。
我们提出一种新型神经网络架构——非训练修改（NTM），用于计算图上随机微分博弈（SDGs）的纳什均衡。这类博弈可建模金融、机器人、能源和社交动态中的广泛图结构多智能体系统，其中智能体在不确定性下进行局部交互。NTM对前馈神经网络施加基于图的稀疏化，嵌入与底层图拓扑对齐的固定非训练组件，提升了可解释性与稳定性，并在大规模稀疏场景下显著减少可训练参数数量。我们理论证明了NTM在静态图博弈中的通用逼近性质，并通过监督学习任务验证其表达能力与鲁棒性。在此基础上，我们将NTM融入两种前沿博弈求解器——直接参数化（DP）与深度后向随机微分方程（Deep BSDE），形成其稀疏变体（NTM-DP与NTM-DBSDE）。在三种不同图结构的SDG上的数值实验表明，基于NTM的方法性能可媲美全训练版本，同时具备更优的计算效率。
原文摘要 · Abstract (English)
We propose a novel neural network architecture, called Non-Trainable Modification (NTM), for computing Nash equilibria in stochastic differential games (SDGs) on graphs. These games model a broad class of graph-structured multi-agent systems arising in finance, robotics, energy, and social dynamics, where agents interact locally under uncertainty. The NTM architecture imposes a graph-guided sparsification on feedforward neural networks, embedding fixed, non-trainable components aligned with the underlying graph topology. This design enhances interpretability and stability, while significantly reducing the number of trainable parameters in large-scale, sparse settings. We theoretically establish a universal approximation property for NTM in static games on graphs and numerically validate its expressivity and robustness through supervised learning tasks. Building on this foundation, we incorporate NTM into two state-of-the-art game solvers, Direct Parameterization and Deep BSDE (backward stochastic differential equation), yielding their sparse variants (NTM-DP and NTM-DBSDE). Numerical experiments on three SDGs across various graph structures demonstrate that NTM-based methods achieve performance comparable to their fully trainable counterparts, while offering improved computational efficiency.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。