Online Optimization with Unknown Time-Varying Parameters from Noisy Gradient Measurements
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866916035789062144 |
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| author | Tripathi, Shivanshu Raissi, Maziar |
| author_facet | Tripathi, Shivanshu Raissi, Maziar |
| contents | We study online optimization problems in which the cost function depends on latent, time-varying parameters that are unmeasurable and governed by unknown dynamics. Specifically, we consider a strongly convex cost function whose linear term evolves according to unknown linear stochastic dynamics, while the algorithm has access only to finite noisy gradient measurements. We propose a solution that uses control theoretic tools to reconstruct the latent parameters from gradient observations using a Gauss-Markov estimator, then identifies the parameter dynamics using an instrumental-variable estimator, and finally forecasts the parameters to compute the future minimizer. We provide a bound on the expected tracking error. We illustrate the effectiveness of our algorithm on a series of numerical examples. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_22251 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Online Optimization with Unknown Time-Varying Parameters from Noisy Gradient Measurements Tripathi, Shivanshu Raissi, Maziar Optimization and Control Systems and Control We study online optimization problems in which the cost function depends on latent, time-varying parameters that are unmeasurable and governed by unknown dynamics. Specifically, we consider a strongly convex cost function whose linear term evolves according to unknown linear stochastic dynamics, while the algorithm has access only to finite noisy gradient measurements. We propose a solution that uses control theoretic tools to reconstruct the latent parameters from gradient observations using a Gauss-Markov estimator, then identifies the parameter dynamics using an instrumental-variable estimator, and finally forecasts the parameters to compute the future minimizer. We provide a bound on the expected tracking error. We illustrate the effectiveness of our algorithm on a series of numerical examples. |
| title | Online Optimization with Unknown Time-Varying Parameters from Noisy Gradient Measurements |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2605.22251 |