Steady-state Based Approach to Online Non-stochastic Control
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_ | 1866914489167773696 |
|---|---|
| author | Hebbar, Vijeth Hutchinson, Spencer Alizadeh, Mahnoosh Langbort, Cédric |
| author_facet | Hebbar, Vijeth Hutchinson, Spencer Alizadeh, Mahnoosh Langbort, Cédric |
| contents | We study the problem of online non-stochastic control (ONC), which is the control of a linear system under adversarial disturbances and adversarial cost functions, with the aim of minimizing the total cost incurred. A recent line of literature in ONC develops algorithms that enjoy sublinear regret with respect to a benchmark based on the set of steady-states that are attainable by a constant input. In this work, we extend this research direction by giving an algorithm that enjoys $\mathcal{O}(\sqrt{T})$ regret with respect to a richer benchmark set, namely the set of steady-states attainable under an \emph{affine controller}. Since this benchmark substantially broadens the comparison class, it provides significantly stronger performance guarantees. Our proposed algorithm combines a Follow-The-Perturbed-Leader-style online non-convex optimization approach with a batching method that maintains stability despite changing policies. Although our proposed algorithm requires solving non-convex subproblems, we show that an approximate solution to this subproblem is sufficient to ensure $\mathcal{O}(\sqrt{T})$ regret. Furthermore, numerical experiments show that our algorithm enjoys lower total cost and similar computation to existing methods in certain settings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_17686 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Steady-state Based Approach to Online Non-stochastic Control Hebbar, Vijeth Hutchinson, Spencer Alizadeh, Mahnoosh Langbort, Cédric Optimization and Control Systems and Control We study the problem of online non-stochastic control (ONC), which is the control of a linear system under adversarial disturbances and adversarial cost functions, with the aim of minimizing the total cost incurred. A recent line of literature in ONC develops algorithms that enjoy sublinear regret with respect to a benchmark based on the set of steady-states that are attainable by a constant input. In this work, we extend this research direction by giving an algorithm that enjoys $\mathcal{O}(\sqrt{T})$ regret with respect to a richer benchmark set, namely the set of steady-states attainable under an \emph{affine controller}. Since this benchmark substantially broadens the comparison class, it provides significantly stronger performance guarantees. Our proposed algorithm combines a Follow-The-Perturbed-Leader-style online non-convex optimization approach with a batching method that maintains stability despite changing policies. Although our proposed algorithm requires solving non-convex subproblems, we show that an approximate solution to this subproblem is sufficient to ensure $\mathcal{O}(\sqrt{T})$ regret. Furthermore, numerical experiments show that our algorithm enjoys lower total cost and similar computation to existing methods in certain settings. |
| title | Steady-state Based Approach to Online Non-stochastic Control |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2604.17686 |