# Optimization as Estimation with Gaussian Processes in Bandit Settings

arXiv: https://arxiv.org/abs/1510.06423 · HTML: https://mlsanity.com/paper/1510.06423/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Oct 2015.

## Built on by (most cited first, 17 of 17)

- [Pre-trained Gaussian Processes for Bayesian Optimization](https://mlsanity.com/paper/2109.08215/) (2021)
- [Randomized Gaussian Process Upper Confidence Bound with Tighter Bayesian Regret Bounds](https://mlsanity.com/paper/2302.01511/) (2023)
- [Posterior Sampling-Based Bayesian Optimization with Tighter Bayesian Regret Bounds](https://mlsanity.com/paper/2311.03760/) (2023)
- [Output Space Entropy Search Framework for Multi-Objective Bayesian Optimization](https://mlsanity.com/paper/2110.06980/) (2021)
- [Learning Regions of Interest for Bayesian Optimization with Adaptive Level-Set Estimation](https://mlsanity.com/paper/2307.13371/) (2023)
- [Batch Bayesian Optimization on Permutations using the Acquisition Weighted Kernel](https://mlsanity.com/paper/2102.13382/) (2021)
- [PF2ES: Parallel Feasible Pareto Frontier Entropy Search for Multi-Objective Bayesian Optimization](https://mlsanity.com/paper/2204.05411/) (2022)
- [TS-RSR: A provably efficient approach for batch Bayesian Optimization](https://mlsanity.com/paper/2403.04764/) (2024)
- [Regret Analysis for Randomized Gaussian Process Upper Confidence Bound](https://mlsanity.com/paper/2409.00979/) (2024)
- [Multi-Fidelity Bayesian Optimization With Across-Task Transferable Max-Value Entropy Search](https://mlsanity.com/paper/2403.09570/) (2024)
- [LITE: Efficiently Estimating Gaussian Probability of Maximality](https://mlsanity.com/paper/2501.13535/) (2025)
- [Uncertainty quantification and exploration-exploitation trade-off in humans](https://mlsanity.com/paper/2102.07647/) (2021)
- [Bayesian Optimization for Macro Placement](https://mlsanity.com/paper/2207.08398/) (2022)
- [Linear Embedding-based High-dimensional Batch Bayesian Optimization without Reconstruction Mappings](https://mlsanity.com/paper/2211.00947/) (2022)
- [Indirect Query Bayesian Optimization with Integrated Feedback](https://mlsanity.com/paper/2412.13559/) (2024)
- [Exploiting Concavity Information in Gaussian Process Contextual Bandit Optimization](https://mlsanity.com/paper/2503.10836/) (2025)
- [Harnessing Heterogeneity: Learning from Decomposed Feedback in Bayesian Modeling](https://mlsanity.com/paper/2107.03003/) (2021)

## Abstract (arXiv)

Recently, there has been rising interest in Bayesian optimization -- the optimization of an unknown function with assumptions usually expressed by a Gaussian Process (GP) prior. We study an optimization strategy that directly uses an estimate of the argmax of the function. This strategy offers both practical and theoretical advantages: no tradeoff parameter needs to be selected, and, moreover, we establish close connections to the popular GP-UCB and GP-PI strategies. Our approach can be understood as automatically and adaptively trading off exploration and exploitation in GP-UCB and GP-PI. We illustrate the effects of this adaptive tuning via bounds on the regret as well as an extensive empirical evaluation on robotics and vision tasks, demonstrating the robustness of this strategy for a range of performance criteria.