提出稀疏反馈策略，让多智能体在信息不全时仍能稳定博弈。
Approximate Feedback Nash Equilibria with Sparse Inter-Agent Dependencies
- 用正则化动态规划找只依赖部分智能体状态的控制策略。
- 在噪声环境下，成本比传统纳什策略降低最多77%。
- 适合通信受限或感知不全的多机器人协同场景。
多智能体动态博弈中的反馈纳什均衡策略需要所有智能体的状态信息来计算控制动作。但在实际场景中，智能体间的感知和通信受限，完全状态反馈代价高昂或不可行，且当其他智能体状态信息不准确时，此类策略易失效。为此，本文提出一种正则化的动态规划方法，用于寻找在动态博弈中仅依赖部分智能体状态的稀疏反馈策略。该方法通过求解凸自适应组Lasso问题，计算逼近纳什均衡解的稀疏策略。我们证明，在线性二次（LQ）博弈中，正则化解渐近收敛至纳什均衡策略的邻域。进一步，通过迭代算法将该方法扩展至一般非LQ博弈。多机器人交互场景的仿真结果表明，所提方法能有效生成具有不同稀疏度的反馈策略。当智能体对其他智能体状态存在噪声观测时，仿真显示该正则化策略相比标准纳什均衡策略，使所有与他人状态耦合的成本降低达77%。
原文摘要 · Abstract (English)
Feedback Nash equilibrium strategies in multi-agent dynamic games require availability of all players' state information to compute control actions. However, in real-world scenarios, sensing and communication limitations between agents make full state feedback expensive or impractical, and such strategies can become fragile when state information from other agents is inaccurate. To this end, we propose a regularized dynamic programming approach for finding sparse feedback policies that selectively depend on the states of a subset of agents in dynamic games. The proposed approach solves convex adaptive group Lasso problems to compute sparse policies approximating Nash equilibrium solutions. We prove the regularized solutions' asymptotic convergence to a neighborhood of Nash equilibrium policies in linear-quadratic (LQ) games. Further, we extend the proposed approach to general non-LQ games via an iterative algorithm. Simulation results in multi-robot interaction scenarios show that the proposed approach effectively computes feedback policies with varying sparsity levels. When agents have noisy observations of other agents' states, simulation results indicate that the proposed regularized policies consistently achieve lower costs than standard Nash equilibrium policies by up to 77% for all interacting agents whose costs are coupled with other agents' states.
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