论文标题
开环通用纳什均衡解决方案的顺序二次编程方法
A Sequential Quadratic Programming Approach to the Solution of Open-Loop Generalized Nash Equilibria
论文作者
论文摘要
动态游戏可能是在多种非合作代理之间建模互动行为的有效方法，并且在这种情况下，它们为同时预测和控制提供了理论框架。在这项工作中，我们提出了一种用于解决非线性动力学和约束代理的开放环通用动力游戏类别的局部通用NASH均衡（GNE）的数值方法。特别是，我们制定了一种顺序二次编程（SQP）方法，该方法仅需要在每次迭代时单个凸二次程序的解决方案。我们方法鲁棒性的核心是一种非单调线搜索方法，也是SQP步骤接受的新功能。我们表明，我们的方法可以在本地GNE附近实现线性收敛，并得出了功能功能的更新规则，该规则有助于从较大的初始条件集中提高收敛性。我们证明了算法在赛车背景下的有效性，在与动态游戏的最先进的解决方案方法进行比较时，我们表现出32 \％的成功率提高。 \ url {https://github.com/zhu-edward/dgsqp}。
Dynamic games can be an effective approach to modeling interactive behavior between multiple non-cooperative agents and they provide a theoretical framework for simultaneous prediction and control in such scenarios. In this work, we propose a numerical method for the solution of local generalized Nash equilibria (GNE) for the class of open-loop general-sum dynamic games for agents with nonlinear dynamics and constraints. In particular, we formulate a sequential quadratic programming (SQP) approach which requires only the solution of a single convex quadratic program at each iteration. Central to the robustness of our approach is a non-monotonic line search method and a novel merit function for SQP step acceptance. We show that our method achieves linear convergence in the neighborhood of local GNE and we derive an update rule for the merit function which helps to improve convergence from a larger set of initial conditions. We demonstrate the effectiveness of the algorithm in the context of car racing, where we show up to 32\% improvement of success rate when comparing against a state-of-the-art solution approach for dynamic games. \url{https://github.com/zhu-edward/DGSQP}.
