Learning in Mean Field Games: A Survey
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arXiv
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| Autori principali: | , , , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866929438710562816 |
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| author | Laurière, Mathieu Perrin, Sarah Pérolat, Julien Girgin, Sertan Muller, Paul Élie, Romuald Geist, Matthieu Pietquin, Olivier |
| author_facet | Laurière, Mathieu Perrin, Sarah Pérolat, Julien Girgin, Sertan Muller, Paul Élie, Romuald Geist, Matthieu Pietquin, Olivier |
| contents | Non-cooperative and cooperative games with a very large number of players have many applications but remain generally intractable when the number of players increases. Introduced by Lasry and Lions, and Huang, Caines and Malhamé, Mean Field Games (MFGs) rely on a mean-field approximation to allow the number of players to grow to infinity. Traditional methods for solving these games generally rely on solving partial or stochastic differential equations with a full knowledge of the model. Recently, Reinforcement Learning (RL) has appeared promising to solve complex problems at scale. The combination of RL and MFGs is promising to solve games at a very large scale both in terms of population size and environment complexity. In this survey, we review the quickly growing recent literature on RL methods to learn equilibria and social optima in MFGs. We first identify the most common settings (static, stationary, and evolutive) of MFGs. We then present a general framework for classical iterative methods (based on best-response computation or policy evaluation) to solve MFGs in an exact way. Building on these algorithms and the connection with Markov Decision Processes, we explain how RL can be used to learn MFG solutions in a model-free way. Last, we present numerical illustrations on a benchmark problem, and conclude with some perspectives. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_12944 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Learning in Mean Field Games: A Survey Laurière, Mathieu Perrin, Sarah Pérolat, Julien Girgin, Sertan Muller, Paul Élie, Romuald Geist, Matthieu Pietquin, Olivier Machine Learning Artificial Intelligence Computer Science and Game Theory Optimization and Control Non-cooperative and cooperative games with a very large number of players have many applications but remain generally intractable when the number of players increases. Introduced by Lasry and Lions, and Huang, Caines and Malhamé, Mean Field Games (MFGs) rely on a mean-field approximation to allow the number of players to grow to infinity. Traditional methods for solving these games generally rely on solving partial or stochastic differential equations with a full knowledge of the model. Recently, Reinforcement Learning (RL) has appeared promising to solve complex problems at scale. The combination of RL and MFGs is promising to solve games at a very large scale both in terms of population size and environment complexity. In this survey, we review the quickly growing recent literature on RL methods to learn equilibria and social optima in MFGs. We first identify the most common settings (static, stationary, and evolutive) of MFGs. We then present a general framework for classical iterative methods (based on best-response computation or policy evaluation) to solve MFGs in an exact way. Building on these algorithms and the connection with Markov Decision Processes, we explain how RL can be used to learn MFG solutions in a model-free way. Last, we present numerical illustrations on a benchmark problem, and conclude with some perspectives. |
| title | Learning in Mean Field Games: A Survey |
| topic | Machine Learning Artificial Intelligence Computer Science and Game Theory Optimization and Control |
| url | https://arxiv.org/abs/2205.12944 |