PDO-Split：一种用于约束势主导博弈的实时求解器
PDO-Split: A Real-Time Solver for Constrained Potential-Dominant Games
- Georgia Institute of Technology（佐治亚理工学院）
机构由 AI 辅助整理，请以论文原文为准。
中文总结 AI 辅助
本文提出PDO-Split，一种针对势主导博弈的实时广义纳什均衡求解器，利用势分量作为预条件器并复用LDL^T分解，显著提升多智能体规划问题的求解速度与收敛性。
中文摘要 AI 辅助
我们提出了势主导算子分裂（PDO-Split），一种用于具有势主导结构的约束动态多智能体问题的实时广义纳什均衡求解器。PDO-Split针对博弈论模型预测控制中的计算瓶颈，在该场景中，随着智能体数量增加，反复求解均衡KKT系统的成本变得高昂。我们引入了一类γ-势主导博弈，其中势（或合作）结构主导了智能体之间的竞争性交互。我们证明，这种结构允许PDO-Split使用势分量作为预条件器，同时通过迭代细化纳入竞争分量。我们建立了收敛保证，并利用势分量的对称性，通过可复用的LDL^T分解来加速线性求解器。我们在多个实际多智能体规划问题中评估了PDO-Split，包括八车赛车和六车匝道合并，与现有的基于DDP和基于牛顿的方法相比，特别是在智能体数量较多时，实现了显著改善的运行时间和收敛速度。该算法还在微型自动驾驶赛车平台上进行了实验验证，展示了该方法的实时能力。
英文摘要
We present Potential-Dominant Operator Splitting (PDO-Split), a real-time generalized Nash equilibrium solver for constrained dynamic multi-agent problems with potential-dominant structure. PDO-Split targets the computational bottleneck in game-theoretic model predictive control, where repeatedly solving the equilibrium KKT system becomes costly as the number of agents increases. We introduce a class of gamma-potential-dominant games, in which the potential (or cooperative) structure dominates the competitive interactions between the agents. We show that this structure allows PDO-Split to use the potential component as a preconditioner while incorporating the competitive component through iterative refinement. We establish convergence guarantees and exploit the symmetry of the potential component through a reusable LDL^T factorization to accelerate the linear solvers. We evaluate PDO-Split across several practical multi-agent planning problems, including eight-car racing and six-vehicle ramp merging, achieving substantially improved runtime and convergence rate over existing DDP-based and Newton-based methods, especially with a larger number of agents. The algorithm is also experimentally validated on miniature autonomous race car platforms, demonstrating the approach's real-time capability.
