提出异构风险偏好下的分布鲁棒博弈均衡求解方法
Wasserstein Distributionally Robust Nash Equilibrium Seeking with Heterogeneous Data: A Lagrangian Approach
- 用拉格朗日法构建异构水波斯特球约束的惩罚机制
- 证明均衡问题等价于强单调变分不等式，可高效求解
- 算法平均遗憾收敛至预设精度，适合多主体鲁棒决策场景
研究一类允许各参与方对不确定性分布偏移具有异构风险厌恶的分布鲁棒博弈。通过拉格朗日形式引入惩罚函数，在每个分布上施加异构的水波斯特球约束。将分布鲁棒纳什均衡问题形式化，并在特定假设下证明其等价于一个具有强单调映射的有限维变分不等式问题。进而设计了一种近似纳什均衡求解算法，证明了平均遗憾随迭代次数增加趋于零，从而以预先设定的精度学习到期望的均衡。数值仿真验证了理论结果的正确性。
原文摘要 · Abstract (English)
We study a class of distributionally robust games where agents are allowed to heterogeneously choose their risk aversion with respect to distributional shifts of the uncertainty. In our formulation, heterogeneous Wasserstein ball constraints on each distribution are enforced through a penalty function leveraging a Lagrangian formulation. We then formulate the distributionally robust Nash equilibrium problem and show that under certain assumptions it is equivalent to a finite-dimensional variational inequality problem with a strongly monotone mapping. We then design an approximate Nash equilibrium seeking algorithm and prove convergence of the average regret to a quantity that diminishes with the number of iterations, thus learning the desired equilibrium up to an a priori specified accuracy. Numerical simulations corroborate our theoretical findings.
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