Mean Field Games on Weighted and Directed Graphs via Colored Digraphons

Fabian, Christian; Cui, Kai; Koeppl, Heinz

doi:10.1109/lcsys.2022.3227453

Cited by 2 publications

(1 citation statement)

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“…However, for sparse graphs, the limiting graphon is not meaningful, making it unsuitable for networks whose degree does not scale with system size, see also [21,18]. MFGs for relatively sparse networks have been studied using Lp-graphs [22], but they too cannot be extended to bounded degrees. We believe that bounded-degree graph modelling is necessary to truly represent and analyse large fixed-degree distributed systems to avoid the need for increasingly global interactions and thus difficulties in scaling.…”

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confidence: 99%

Learning Mean-Field Control for Delayed Information Load Balancing in Large Queuing Systems

Tahir

Cui

Koeppl

2022

Proceedings of the 51st International Conference on Parallel Processing

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Scalable load balancing algorithms are of great interest in cloud networks and data centers, necessitating the use of tractable techniques to compute optimal load balancing policies for good performance. However, most existing scalable techniques, especially asymptotically scaling methods based on mean field theory, have not been able to model large queueing networks with strong locality. Meanwhile, general multi-agent reinforcement learning techniques can be hard to scale and usually lack a theoretical foundation. In this work, we address this challenge by leveraging recent advances in sparse mean field theory to learn a near-optimal load balancing policy in sparsely connected queueing networks in a tractable manner, which may be preferable to global approaches in terms of communication overhead. Importantly, we obtain a general load balancing framework for a large class of sparse bounded-degree topologies. By formulating a novel mean field control problem in the context of graphs with bounded degree, we reduce the otherwise difficult multi-agent problem to a single-agent problem. Theoretically, the approach is justified by approximation guarantees. Empirically, the proposed methodology performs well on several realistic and scalable network topologies. Moreover, we compare it with a number of well-known load balancing heuristics and with existing scalable multi-agent reinforcement learning methods. Overall, we obtain a tractable approach for load balancing in highly localized networks.

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confidence: 99%