A Variational Inequality Approach to Independent Learning in Static Mean-Field Games
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915134232854528 |
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| author | Yardim, Batuhan Cayci, Semih He, Niao |
| author_facet | Yardim, Batuhan Cayci, Semih He, Niao |
| contents | Competitive games involving thousands or even millions of players are prevalent in real-world contexts, such as transportation, communications, and computer networks. However, learning in these large-scale multi-agent environments presents a grand challenge, often referred to as the "curse of many agents". In this paper, we formalize and analyze the Static Mean-Field Game (SMFG) under both full and bandit feedback, offering a generic framework for modeling large population interactions while enabling independent learning.
We first establish close connections between SMFG and variational inequality (VI), showing that SMFG can be framed as a VI problem in the infinite agent limit. Building on the VI perspective, we propose independent learning and exploration algorithms that efficiently converge to approximate Nash equilibria, when dealing with a finite number of agents. Theoretically, we provide explicit finite sample complexity guarantees for independent learning across various feedback models in repeated play scenarios, assuming (strongly-)monotone payoffs. Numerically, we validate our results through both simulations and real-world applications in city traffic and network access management. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_00915 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Variational Inequality Approach to Independent Learning in Static Mean-Field Games Yardim, Batuhan Cayci, Semih He, Niao Optimization and Control Computer Science and Game Theory Competitive games involving thousands or even millions of players are prevalent in real-world contexts, such as transportation, communications, and computer networks. However, learning in these large-scale multi-agent environments presents a grand challenge, often referred to as the "curse of many agents". In this paper, we formalize and analyze the Static Mean-Field Game (SMFG) under both full and bandit feedback, offering a generic framework for modeling large population interactions while enabling independent learning. We first establish close connections between SMFG and variational inequality (VI), showing that SMFG can be framed as a VI problem in the infinite agent limit. Building on the VI perspective, we propose independent learning and exploration algorithms that efficiently converge to approximate Nash equilibria, when dealing with a finite number of agents. Theoretically, we provide explicit finite sample complexity guarantees for independent learning across various feedback models in repeated play scenarios, assuming (strongly-)monotone payoffs. Numerically, we validate our results through both simulations and real-world applications in city traffic and network access management. |
| title | A Variational Inequality Approach to Independent Learning in Static Mean-Field Games |
| topic | Optimization and Control Computer Science and Game Theory |
| url | https://arxiv.org/abs/2502.00915 |