# No-regret Algorithms for Multi-task Bayesian Optimization

arXiv: https://arxiv.org/abs/2008.08885 · HTML: https://mlsanity.com/paper/2008.08885/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Aug 2020.

## Built on by (most cited first, 18 of 18)

- [Bayesian Optimization with High-Dimensional Outputs](https://mlsanity.com/paper/2106.12997/) (2021)
- [Provably Efficient Cooperative Multi-Agent Reinforcement Learning with Function Approximation](https://mlsanity.com/paper/2103.04972/) (2021)
- [Evolutionary Multitask Optimization: a Methodological Overview, Challenges and Future Research Directions](https://mlsanity.com/paper/2102.02558/) (2021)
- [Unleashing LLMs in Bayesian Optimization: Preference-Guided Framework for Scientific Discovery](https://mlsanity.com/paper/2605.17976/) (2026)
- [Multitask Learning with No Regret: from Improved Confidence Bounds to Active Learning](https://mlsanity.com/paper/2308.01744/) (2023)
- [Pseudo-Bayesian Optimization](https://mlsanity.com/paper/2310.09766/) (2023)
- [Regret Bounds for Noise-Free Cascaded Kernelized Bandits](https://mlsanity.com/paper/2211.05430/) (2022)
- [Multi-objective optimisation via the R2 utilities](https://mlsanity.com/paper/2305.11774/) (2023)
- [Scalable Bayesian optimization with high-dimensional outputs using randomized prior networks](https://mlsanity.com/paper/2302.07260/) (2023)
- [A Hierarchical Surrogate Model for Efficient Multi-Task Parameter Learning in Closed-Loop Control](https://mlsanity.com/paper/2508.12738/) (2025)
- [Function-on-Function Bayesian Optimization](https://mlsanity.com/paper/2511.12783/) (2025)
- [Bayesian Optimization with Structured Measurements: A Vector-Valued RKHS Framework](https://mlsanity.com/paper/2605.09775/) (2026)
- [Nearly-Optimal Algorithm for Adversarial Kernelized Bandits](https://mlsanity.com/paper/2605.10299/) (2026)
- [OptEx: Expediting First-Order Optimization with Approximately Parallelized Iterations](https://mlsanity.com/paper/2402.11427/) (2024)
- [Kernel conditional tests from learning-theoretic bounds](https://mlsanity.com/paper/2506.03898/) (2025)
- [Combinatorial Bandit Bayesian Optimization for Tensor Outputs](https://mlsanity.com/paper/2602.00640/) (2026)
- [Sequential operator learning under dependent data](https://mlsanity.com/paper/2608.24426/) (2026)
- [Adapting Nonstationary Multi-output Gaussian Processes to Bayesian Optimization](https://mlsanity.com/paper/2609.32464/) (2026)

## Abstract (arXiv)

We consider multi-objective optimization (MOO) of an unknown vector-valued function in the non-parametric Bayesian optimization (BO) setting, with the aim being to learn points on the Pareto front of the objectives. Most existing BO algorithms do not model the fact that the multiple objectives, or equivalently, tasks can share similarities, and even the few that do lack rigorous, finite-time regret guarantees that capture explicitly inter-task structure. In this work, we address this problem by modelling inter-task dependencies using a multi-task kernel and develop two novel BO algorithms based on random scalarizations of the objectives. Our algorithms employ vector-valued kernel regression as a stepping stone and belong to the upper confidence bound class of algorithms. Under a smoothness assumption that the unknown vector-valued function is an element of the reproducing kernel Hilbert space associated with the multi-task kernel, we derive worst-case regret bounds for our algorithms that explicitly capture the similarities between tasks. We numerically benchmark our algorithms on both synthetic and real-life MOO problems, and show the advantages offered by learning with multi-task kernels.