# Time-Varying Optimization of Networked Systems with Human Preferences

arXiv: https://arxiv.org/abs/2103.13470 · HTML: https://mlsanity.com/paper/2103.13470/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Mar 2021.

## Built on by (most cited first, 4 of 4)

- [Personalized incentives as feedback design in generalized Nash equilibrium problems](https://mlsanity.com/paper/2203.12948/) (2022)
- [A Survey on Distributed Online Optimization and Game](https://mlsanity.com/paper/2205.00473/) (2022)
- [The Nah Bandit: Modeling User Non-compliance in Recommendation Systems](https://mlsanity.com/paper/2408.07897/) (2024)
- [Online Learning with Multiple Fairness Regularizers via Graph-Structured Feedback](https://mlsanity.com/paper/2508.14311/) (2025)

## Abstract (arXiv)

This paper considers a time-varying optimization problem associated with a network of systems, with each of the systems shared by (and affecting) a number of individuals. The objective is to minimize cost functions associated with the individuals' preferences, which are unknown, subject to time-varying constraints that capture physical or operational limits of the network. To this end, the paper develops a distributed online optimization algorithm with concurrent learning of the cost functions. The cost functions are learned on-the-fly based on the users' feedback (provided at irregular intervals) by leveraging tools from shape-constrained Gaussian Process. The online algorithm is based on a primal-dual method, and acts effectively in a closed-loop fashion where: i) users' feedback is utilized to estimate the cost, and ii) measurements from the network are utilized in the algorithmic steps to bypass the need for sensing of (unknown) exogenous inputs of the network. The performance of the algorithm is analyzed in terms of dynamic network regret and constraint violation. Numerical examples are presented in the context of real-time optimization of distributed energy resources.