Online Min-Max Optimization: From Individual Regrets to Cumulative Saddle Points
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866918332056207360 |
|---|---|
| author | Vyas, Abhijeet Bullins, Brian |
| author_facet | Vyas, Abhijeet Bullins, Brian |
| contents | We propose and study an online version of min-max optimization based on cumulative saddle points under a variety of performance measures beyond convex-concave settings. After first observing the incompatibility of (static) Nash equilibrium (SNE-Reg$_T$) with individual regrets even for strongly convex-strongly concave functions, we propose an alternate \emph{static} duality gap (SDual-Gap$_T$) inspired by the online convex optimization (OCO) framework. We provide algorithms that, using a reduction to classic OCO problems, achieve bounds for SDual-Gap$_T$~and a novel \emph{dynamic} saddle point regret (DSP-Reg$_T$), which we suggest naturally represents a min-max version of the dynamic regret in OCO. We derive our bounds for SDual-Gap$_T$~and DSP-Reg$_T$~under strong convexity-strong concavity and a min-max notion of exponential concavity (min-max EC), and in addition we establish a class of functions satisfying min-max EC~that captures a two-player variant of the classic portfolio selection problem. Finally, for a dynamic notion of regret compatible with individual regrets, we derive bounds under a two-sided Polyak-Łojasiewicz (PL) condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_10565 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Online Min-Max Optimization: From Individual Regrets to Cumulative Saddle Points Vyas, Abhijeet Bullins, Brian Machine Learning Optimization and Control We propose and study an online version of min-max optimization based on cumulative saddle points under a variety of performance measures beyond convex-concave settings. After first observing the incompatibility of (static) Nash equilibrium (SNE-Reg$_T$) with individual regrets even for strongly convex-strongly concave functions, we propose an alternate \emph{static} duality gap (SDual-Gap$_T$) inspired by the online convex optimization (OCO) framework. We provide algorithms that, using a reduction to classic OCO problems, achieve bounds for SDual-Gap$_T$~and a novel \emph{dynamic} saddle point regret (DSP-Reg$_T$), which we suggest naturally represents a min-max version of the dynamic regret in OCO. We derive our bounds for SDual-Gap$_T$~and DSP-Reg$_T$~under strong convexity-strong concavity and a min-max notion of exponential concavity (min-max EC), and in addition we establish a class of functions satisfying min-max EC~that captures a two-player variant of the classic portfolio selection problem. Finally, for a dynamic notion of regret compatible with individual regrets, we derive bounds under a two-sided Polyak-Łojasiewicz (PL) condition. |
| title | Online Min-Max Optimization: From Individual Regrets to Cumulative Saddle Points |
| topic | Machine Learning Optimization and Control |
| url | https://arxiv.org/abs/2602.10565 |