Inverse learning of black-box aggregator for robust Nash equilibrium
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866917616410427392 |
|---|---|
| author | Chen, Guanpu Xu, Gehui He, Fengxiang Tao, Dacheng Parisini, Thomas Johansson, Karl Henrik |
| author_facet | Chen, Guanpu Xu, Gehui He, Fengxiang Tao, Dacheng Parisini, Thomas Johansson, Karl Henrik |
| contents | In this note, we investigate the robustness of Nash equilibria (NE) in multi-player aggregative games with coupling constraints. There are many algorithms for computing an NE of an aggregative game given a known aggregator. When the coupling parameters are affected by uncertainty, robust NE need to be computed. We consider a scenario where players' weight in the aggregator is unknown, making the aggregator kind of "a black box". We pursue a suitable learning approach to estimate the unknown aggregator by proposing an inverse variational inequality-based relationship. We then utilize the counterpart to reconstruct the game and obtain first-order conditions for robust NE in the worst case. Furthermore, we characterize the generalization property of the learning methodology via an upper bound on the violation probability. Simulation experiments show the effectiveness of the proposed inverse learning approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_10980 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Inverse learning of black-box aggregator for robust Nash equilibrium Chen, Guanpu Xu, Gehui He, Fengxiang Tao, Dacheng Parisini, Thomas Johansson, Karl Henrik Computer Science and Game Theory Systems and Control Optimization and Control In this note, we investigate the robustness of Nash equilibria (NE) in multi-player aggregative games with coupling constraints. There are many algorithms for computing an NE of an aggregative game given a known aggregator. When the coupling parameters are affected by uncertainty, robust NE need to be computed. We consider a scenario where players' weight in the aggregator is unknown, making the aggregator kind of "a black box". We pursue a suitable learning approach to estimate the unknown aggregator by proposing an inverse variational inequality-based relationship. We then utilize the counterpart to reconstruct the game and obtain first-order conditions for robust NE in the worst case. Furthermore, we characterize the generalization property of the learning methodology via an upper bound on the violation probability. Simulation experiments show the effectiveness of the proposed inverse learning approach. |
| title | Inverse learning of black-box aggregator for robust Nash equilibrium |
| topic | Computer Science and Game Theory Systems and Control Optimization and Control |
| url | https://arxiv.org/abs/2403.10980 |