Beyond Asymptotics: Targeted exploration with finite-sample guarantees
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866915939026468864 |
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| author | Venkatasubramanian, Janani Köhler, Johannes Allgöwer, Frank |
| author_facet | Venkatasubramanian, Janani Köhler, Johannes Allgöwer, Frank |
| contents | In this paper, we introduce a targeted exploration strategy for the non-asymptotic, finite-time case. The proposed strategy is applicable to uncertain linear time-invariant systems subject to sub-Gaussian disturbances. As the main result, the proposed approach provides a priori guarantees, ensuring that the optimized exploration inputs achieve a desired accuracy of the model parameters. The technical derivation of the strategy (i) leverages existing non-asymptotic identification bounds with self-normalized martingales, (ii) utilizes spectral lines to predict the effect of sinusoidal excitation, and (iii) effectively accounts for spectral transient error and parametric uncertainty. A numerical example illustrates how the finite exploration time influence the required exploration energy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_02380 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Beyond Asymptotics: Targeted exploration with finite-sample guarantees Venkatasubramanian, Janani Köhler, Johannes Allgöwer, Frank Systems and Control In this paper, we introduce a targeted exploration strategy for the non-asymptotic, finite-time case. The proposed strategy is applicable to uncertain linear time-invariant systems subject to sub-Gaussian disturbances. As the main result, the proposed approach provides a priori guarantees, ensuring that the optimized exploration inputs achieve a desired accuracy of the model parameters. The technical derivation of the strategy (i) leverages existing non-asymptotic identification bounds with self-normalized martingales, (ii) utilizes spectral lines to predict the effect of sinusoidal excitation, and (iii) effectively accounts for spectral transient error and parametric uncertainty. A numerical example illustrates how the finite exploration time influence the required exploration energy. |
| title | Beyond Asymptotics: Targeted exploration with finite-sample guarantees |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2504.02380 |