大群体中混合学习规则的无源性工具
Passivity Tools for Hybrid Learning Rules in Large Populations
AI总结：
针对大群体中智能体非典范类混合学习规则的均衡稳定性分析问题，本文提出更通用的可处理不连续规则的$\delta$-无源性版本，证明两类混合学习规则凸锥满足该无源性，两策略场景下可合并保无源性，并用数值算例验证了适用性。
摘要：
近期研究开创性地运用系统理论中的无源性，来研究大群体学习智能体中非合作策略互动动力学的均衡稳定性。在该研究及相关工作中，稳定性分析依赖于如下认知：用于建模智能体策略行为的某些“典范”类学习规则满足一种被称为$\delta$-无源性的无源性条件。本文中，我们考虑智能体展现出的学习行为不符合典范类别的情况。具体而言，我们聚焦于刻画结合了典范类元素的混合学习规则的$\delta$-无源性。我们的分析还引入并使用了一种更具一般性的$\delta$-无源性版本，该版本首次能够处理不连续学习规则，包括表现出最优响应行为的规则。我们陈述并证明了为两类宽泛的混合学习规则凸锥确立$\delta$-无源性的定理。在仅涉及两种策略的场景中，这些凸锥可合并为一个更大的凸锥且仍保持$\delta$-无源性。在证明过程中，我们确立了若干本身具有重要意义、且有可能用于进一步推广本研究的中间结论。我们通过数值算例说明了研究结果的适用性。
英文摘要：
Recent work has pioneered the use of system-theoretic passivity to study equilibrium stability for the dynamics of noncooperative strategic interactions in large populations of learning agents. In this and related works, the stability analysis leverages knowledge that certain ``canonical'' classes of learning rules used to model the agents' strategic behaviors satisfy a passivity condition known as $δ$-passivity. In this paper, we consider that agents exhibit learning behaviors that do not align with a canonical class. Specifically, we focus on characterizing $δ$-passivity for hybrid learning rules that combine elements from canonical classes. Our analysis also introduces and uses a more general version of $δ$-passivity, which, for the first time, can handle discontinuous learning rules, including those showing best-response behaviors. We state and prove theorems establishing $δ$-passivity for two broad convex cones of hybrid learning rules. These cones can merge into a larger one preserving $δ$-passivity in scenarios limited to two strategies. In our proofs, we establish intermediate facts that are significant on their own and could potentially be used to further generalize our work. We illustrate the applicability of our results through numerical examples.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
