Continuous-time Discounted Mirror-Descent Dynamics in Monotone Concave Games
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2019
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866909369371721728 |
|---|---|
| author | Gao, Bolin Pavel, Lacra |
| author_facet | Gao, Bolin Pavel, Lacra |
| contents | In this paper, we consider concave continuous-kernel games characterized by monotonicity properties and propose discounted mirror descent-type dynamics. We introduce two classes of dynamics whereby the associated mirror map is constructed based on a strongly convex or a Legendre regularizer. Depending on the properties of the regularizer we show that these new dynamics can converge asymptotically in concave games with monotone (negative) pseudo-gradient. Furthermore, we show that when the regularizer enjoys strong convexity, the resulting dynamics can converge even in games with hypo-monotone (negative) pseudo-gradient, which corresponds to a shortage of monotonicity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1912_03460 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Continuous-time Discounted Mirror-Descent Dynamics in Monotone Concave Games Gao, Bolin Pavel, Lacra Optimization and Control Computer Science and Game Theory Machine Learning Multiagent Systems Systems and Control In this paper, we consider concave continuous-kernel games characterized by monotonicity properties and propose discounted mirror descent-type dynamics. We introduce two classes of dynamics whereby the associated mirror map is constructed based on a strongly convex or a Legendre regularizer. Depending on the properties of the regularizer we show that these new dynamics can converge asymptotically in concave games with monotone (negative) pseudo-gradient. Furthermore, we show that when the regularizer enjoys strong convexity, the resulting dynamics can converge even in games with hypo-monotone (negative) pseudo-gradient, which corresponds to a shortage of monotonicity. |
| title | Continuous-time Discounted Mirror-Descent Dynamics in Monotone Concave Games |
| topic | Optimization and Control Computer Science and Game Theory Machine Learning Multiagent Systems Systems and Control |
| url | https://arxiv.org/abs/1912.03460 |