Online Optimization with Unknown Time-Varying Parameters Using Noisy Gradient Measurements
Abstract
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 about an unknown nominal operating point, 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 a bias-reduced instrumental variable estimator, and finally forecasts the parameters to compute the minimizer. We provide a high probability, finite-horizon bound on the expected tracking error. We illustrate our algorithm on a series of numerical examples.
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BibTeX
@misc{tripathi2026online,
title = {{Online Optimization with Unknown Time-Varying Parameters Using Noisy Gradient Measurements}},
author = {Shivanshu Tripathi and Fabio Pasqualetti and Maziar Raissi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.22251},
eprint = {2605.22251},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.22251},
}
RIS
TY - UNPB
TI - Online Optimization with Unknown Time-Varying Parameters Using Noisy Gradient Measurements
AU - Shivanshu Tripathi
AU - Fabio Pasqualetti
AU - Maziar Raissi
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2605.22251
UR - https://arxiv.org/abs/2605.22251
AB - 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 about an unknown nominal operating point, 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 a bias-reduced instrumental variable estimator, and finally forecasts the parameters to compute the minimizer. We provide a high probability, finite-horizon bound on the expected tracking error. We illustrate our algorithm on a series of numerical examples.
ER -