Optimistic Online Learning in Symmetric Cone Games
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866915826320277504 |
|---|---|
| author | Barakat, Anas Lin, Wayne Lazarsfeld, John Varvitsiotis, Antonios |
| author_facet | Barakat, Anas Lin, Wayne Lazarsfeld, John Varvitsiotis, Antonios |
| contents | We introduce symmetric cone games (SCGs), a broad class of multi-player games where each player's strategy lies in a generalized simplex (the trace-one slice of a symmetric cone). This framework unifies a wide spectrum of settings, including normal-form games (simplex strategies), quantum games (density matrices), and continuous games with ball-constrained strategies. It also captures several structured machine learning and optimization problems, such as distance metric learning and Fermat-Weber facility location, as two-player zero-sum SCGs. To compute approximate Nash equilibria in two-player zero-sum SCGs, we propose a single online learning algorithm: Optimistic Symmetric Cone Multiplicative Weights Updates (OSCMWU). Unlike prior methods tailored to specific geometries, OSCMWU provides closed-form updates over any symmetric cone and achieves a $\tilde{\mathcal{O}}(1/ε)$ iteration complexity for computing $ε$-saddle points. Our analysis builds on the Optimistic Follow-the-Regularized-Leader framework and hinges on a key technical contribution: We prove that the symmetric cone negative entropy is strongly convex with respect to the trace-one norm. This result extends known results for the simplex and spectraplex to all symmetric cones, and may be of independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_03592 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimistic Online Learning in Symmetric Cone Games Barakat, Anas Lin, Wayne Lazarsfeld, John Varvitsiotis, Antonios Optimization and Control Computer Science and Game Theory Machine Learning We introduce symmetric cone games (SCGs), a broad class of multi-player games where each player's strategy lies in a generalized simplex (the trace-one slice of a symmetric cone). This framework unifies a wide spectrum of settings, including normal-form games (simplex strategies), quantum games (density matrices), and continuous games with ball-constrained strategies. It also captures several structured machine learning and optimization problems, such as distance metric learning and Fermat-Weber facility location, as two-player zero-sum SCGs. To compute approximate Nash equilibria in two-player zero-sum SCGs, we propose a single online learning algorithm: Optimistic Symmetric Cone Multiplicative Weights Updates (OSCMWU). Unlike prior methods tailored to specific geometries, OSCMWU provides closed-form updates over any symmetric cone and achieves a $\tilde{\mathcal{O}}(1/ε)$ iteration complexity for computing $ε$-saddle points. Our analysis builds on the Optimistic Follow-the-Regularized-Leader framework and hinges on a key technical contribution: We prove that the symmetric cone negative entropy is strongly convex with respect to the trace-one norm. This result extends known results for the simplex and spectraplex to all symmetric cones, and may be of independent interest. |
| title | Optimistic Online Learning in Symmetric Cone Games |
| topic | Optimization and Control Computer Science and Game Theory Machine Learning |
| url | https://arxiv.org/abs/2504.03592 |