Online Feedback Optimization for Constrained Stochastic Problems with Decision-Dependent Distributions
Abstract
Online feedback optimization (OFO) leverages real-time output measurements to optimize the operation of networked systems without requiring full knowledge of system dynamics or disturbances. We develop an OFO approach for constrained stochastic optimization problems in which the distribution of the system's random parameters shifts in response to the control actions. We propose a projected primal-dual algorithm where the true dual constraint sets are replaced by surrogate sets. Our main result is an upper bound on the mean-square tracking error, which decomposes into four interpretable terms reflecting: (i) the stochasticity of the problem, (ii) output measurement errors, (iii) time-variability of the problem, and (iv) the mismatch between surrogate and true dual constraint sets. The theory is illustrated in a numerical experiment for power grids with price-responsive assets.
Related
- Discrete-time feedback linearization control for nonsmooth constrained optimization
- Stochastic Sequential Feedback Optimization for Wind Farm Control under Time-Varying Inflow
- A Stochastic Proximal-Gradient Method for Regularized Generally Constrained Continuous Optimization
- A Unified Efficient Gradient-Based Heuristic For Box-Constrained Expectation-Related and Risk-Averse Stochastic Optimization Problems
- Stochastic Appointment Scheduling with Patient-and-Time-Dependent Probability Distributions
BibTeX
@misc{lauand2026online,
title = {{Online Feedback Optimization for Constrained Stochastic Problems with Decision-Dependent Distributions}},
author = {Caio Kalil Lauand and Emiliano Dall'Anese},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.19284},
eprint = {2606.19284},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.19284},
}
RIS
TY - UNPB
TI - Online Feedback Optimization for Constrained Stochastic Problems with Decision-Dependent Distributions
AU - Caio Kalil Lauand
AU - Emiliano Dall'Anese
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2606.19284
UR - https://arxiv.org/abs/2606.19284
AB - Online feedback optimization (OFO) leverages real-time output measurements to optimize the operation of networked systems without requiring full knowledge of system dynamics or disturbances. We develop an OFO approach for constrained stochastic optimization problems in which the distribution of the system's random parameters shifts in response to the control actions. We propose a projected primal-dual algorithm where the true dual constraint sets are replaced by surrogate sets. Our main result is an upper bound on the mean-square tracking error, which decomposes into four interpretable terms reflecting: (i) the stochasticity of the problem, (ii) output measurement errors, (iii) time-variability of the problem, and (iv) the mismatch between surrogate and true dual constraint sets. The theory is illustrated in a numerical experiment for power grids with price-responsive assets.
ER -