Online Optimization with Unknown Time-Varying Parameters from Noisy Gradient Measurements

Fuente: arXiv
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Main Authors: Tripathi, Shivanshu, Raissi, Maziar
Format: Preprint
Published: 2026
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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
id 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