论文标题
通过彩色挖掘者在加权和定向图上的平均野外游戏
Mean Field Games on Weighted and Directed Graphs via Colored Digraphons
论文作者
论文摘要
多机构增强学习（MARL）的领域已通过采用各种学习方法来控制具有挑战性的多代理系统。这些方法中有许多方法集中在Marl问题的经验和算法方面，并且缺乏严格的理论基础。另一方面，Graphon平均现场游戏（GMFGS）为学习问题提供了可扩展且数学上有充分根据的方法，涉及大量连接的代理。在标准GMFG中，代理之间的连接是随着时间的推移而定向，未加权和不变的。我们的论文介绍了彩色的Digraphon平均野战游戏（CDMFG），该游戏允许在随着时间的推移随着时间的推移而自适应的代理之间进行加权和定向链接。因此，与标准GMFG相比，CDMFG能够建模更复杂的连接。除了进行严格的理论分析（包括存在和融合保证）外，我们还提供了学习计划，并通过流行病模型和金融市场中系统性风险的模型来说明我们的发现。
The field of multi-agent reinforcement learning (MARL) has made considerable progress towards controlling challenging multi-agent systems by employing various learning methods. Numerous of these approaches focus on empirical and algorithmic aspects of the MARL problems and lack a rigorous theoretical foundation. Graphon mean field games (GMFGs) on the other hand provide a scalable and mathematically well-founded approach to learning problems that involve a large number of connected agents. In standard GMFGs, the connections between agents are undirected, unweighted and invariant over time. Our paper introduces colored digraphon mean field games (CDMFGs) which allow for weighted and directed links between agents that are also adaptive over time. Thus, CDMFGs are able to model more complex connections than standard GMFGs. Besides a rigorous theoretical analysis including both existence and convergence guarantees, we provide a learning scheme and illustrate our findings with an epidemics model and a model of the systemic risk in financial markets.
