# Personalized Optimization with User's Feedback

arXiv: https://arxiv.org/abs/1905.00775 · HTML: https://mlsanity.com/paper/1905.00775/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 May 2019.

## Built on by (most cited first, 5 of 5)

- [Learning equilibria with personalized incentives in a class of nonmonotone games](https://mlsanity.com/paper/2111.03854/) (2021)
- [OpReg-Boost: Learning to Accelerate Online Algorithms with Operator Regression](https://mlsanity.com/paper/2105.13271/) (2021)
- [Personalized incentives as feedback design in generalized Nash equilibrium problems](https://mlsanity.com/paper/2203.12948/) (2022)
- [No-regret learning for repeated non-cooperative games with lossy bandits](https://mlsanity.com/paper/2205.06968/) (2022)
- [Achievement and Fragility of Long-term Equitability](https://mlsanity.com/paper/2206.12333/) (2022)

## Abstract (arXiv)

This paper develops an online algorithm to solve a time-varying optimization problem with an objective that comprises a known time-varying cost and an unknown function. This problem structure arises in a number of engineering systems and cyber-physical systems where the known function captures time-varying engineering costs, and the unknown function models user's satisfaction; in this context, the objective is to strike a balance between given performance metrics and user's satisfaction. Key challenges related to the problem at hand are related to (1) the time variability of the problem, and (2) the fact that learning of the user's utility function is performed concurrently with the execution of the online algorithm. This paper leverages Gaussian processes (GP) to learn the unknown cost function from noisy functional evaluation and build pertinent upper confidence bounds. Using the GP formalism, the paper then advocates time-varying optimization tools to design an online algorithm that exhibits tracking of the oracle-based optimal trajectory within an error ball, while learning the user's satisfaction function with no-regret. The algorithmic steps are inexact, to account for possible limited computational budgets or real-time implementation considerations. Numerical examples are illustrated based on a problem related to vehicle platooning.