# Primal-Dual Contextual Bayesian Optimization for Control System Online Optimization with Time-Average Constraints

arXiv: https://arxiv.org/abs/2304.06104 · HTML: https://mlsanity.com/paper/2304.06104/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 31 references that are in the map.
- First posted on arXiv 12 Apr 2023.

## Builds on (most cited first, 17 of 17)

- [On Kernelized Multi-armed Bandits](https://mlsanity.com/paper/1704.00445/) (2017)
- [On Information Gain and Regret Bounds in Gaussian Process Bandits](https://mlsanity.com/paper/2009.06966/) (2020)
- [Bayesian Optimization with Safety Constraints: Safe and Automatic Parameter Tuning in Robotics](https://mlsanity.com/paper/1602.04450/) (2016)
- [Bayesian Optimization with Unknown Constraints](https://mlsanity.com/paper/1403.5607/) (2014)
- [Stagewise Safe Bayesian Optimization with Gaussian Processes](https://mlsanity.com/paper/1806.07555/) (2018)
- [What Doubling Tricks Can and Can't Do for Multi-Armed Bandits](https://mlsanity.com/paper/1803.06971/) (2018)
- [Time-Varying Gaussian Process Bandit Optimization](https://mlsanity.com/paper/1601.06650/) (2016)
- [Constrained Efficient Global Optimization of Expensive Black-box Functions](https://mlsanity.com/paper/2211.00162/) (2022)
- [Weighted Gaussian Process Bandits for Non-stationary Environments](https://mlsanity.com/paper/2107.02371/) (2021)
- [GoSafe: Globally Optimal Safe Robot Learning](https://mlsanity.com/paper/2105.13281/) (2021)
- [Safe Contextual Bayesian Optimization for Sustainable Room Temperature PID Control Tuning](https://mlsanity.com/paper/1906.12086/) (2019)
- [On Kernelized Multi-Armed Bandits with Constraints](https://mlsanity.com/paper/2203.15589/) (2022)
- [On Controller Tuning with Time-Varying Bayesian Optimization](https://mlsanity.com/paper/2207.11120/) (2022)
- [VABO: Violation-Aware Bayesian Optimization for Closed-Loop Control Performance Optimization with Unmodeled Constraints](https://mlsanity.com/paper/2110.07479/) (2021)
- [Performance-based Trajectory Optimization for Path Following Control Using Bayesian Optimization](https://mlsanity.com/paper/2103.15416/) (2021)
- [Lower Bounds on the Worst-Case Complexity of Efficient Global Optimization](https://mlsanity.com/paper/2209.09655/) (2022)
- [Violation-Aware Contextual Bayesian Optimization for Controller Performance Optimization with Unmodeled Constraints](https://mlsanity.com/paper/2301.12099/) (2023)

## Built on by (most cited first, 3 of 3)

- [Safe Time-Varying Optimization based on Gaussian Processes with Spatio-Temporal Kernel](https://mlsanity.com/paper/2409.18000/) (2024)
- [Data-driven adaptive building thermal controller tuning with constraints: A primal-dual contextual Bayesian optimization approach](https://mlsanity.com/paper/2310.00758/) (2023)
- [Local Constrained Bayesian Optimization](https://mlsanity.com/paper/2603.07965/) (2026)

## Abstract (arXiv)

This paper studies the problem of online performance optimization of constrained closed-loop control systems, where both the objective and the constraints are unknown black-box functions affected by exogenous time-varying contextual disturbances. A primal-dual contextual Bayesian optimization algorithm is proposed that achieves sublinear cumulative regret with respect to the dynamic optimal solution under certain regularity conditions. Furthermore, the algorithm achieves zero time-average constraint violation, ensuring that the average value of the constraint function satisfies the desired constraint. The method is applied to both sampled instances from Gaussian processes and a continuous stirred tank reactor parameter tuning problem; simulation results show that the method simultaneously provides close-to-optimal performance and maintains constraint feasibility on average. This contrasts current state-of-the-art methods, which either suffer from large cumulative regret or severe constraint violations for the case studies presented.