# Gaussian Process Optimization with Mutual Information

arXiv: https://arxiv.org/abs/1311.4825 · HTML: https://mlsanity.com/paper/1311.4825/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Nov 2013.

## Built on by (most cited first, 11 of 11)

- [Pre-trained Gaussian Processes for Bayesian Optimization](https://mlsanity.com/paper/2109.08215/) (2021)
- [Information-Theoretic Safe Exploration with Gaussian Processes](https://mlsanity.com/paper/2212.04914/) (2022)
- [Collaborative and Distributed Bayesian Optimization via Consensus: Showcasing the Power of Collaboration for Optimal Design](https://mlsanity.com/paper/2306.14348/) (2023)
- [End-to-End Learning of Deep Kernel Acquisition Functions for Bayesian Optimization](https://mlsanity.com/paper/2111.00639/) (2021)
- [Using Distance Correlation for Efficient Bayesian Optimization](https://mlsanity.com/paper/2102.08993/) (2021)
- [Batched Stochastic Bandit for Nondegenerate Functions](https://mlsanity.com/paper/2405.05733/) (2024)
- [Stochastic Path Planning in Correlated Obstacle Fields](https://mlsanity.com/paper/2509.19559/) (2025)
- [Harnessing Heterogeneity: Learning from Decomposed Feedback in Bayesian Modeling](https://mlsanity.com/paper/2107.03003/) (2021)
- [Information-Theoretic Safe Bayesian Optimization](https://mlsanity.com/paper/2402.15347/) (2024)
- [Multi-Output Gaussian Processes for Graph-Structured Data](https://mlsanity.com/paper/2505.16755/) (2025)
- [A Constrained Multi-Fidelity Bayesian Optimization Method](https://mlsanity.com/paper/2510.10984/) (2025)

## Abstract (arXiv)

In this paper, we analyze a generic algorithm scheme for sequential global optimization using Gaussian processes. The upper bounds we derive on the cumulative regret for this generic algorithm improve by an exponential factor the previously known bounds for algorithms like GP-UCB. We also introduce the novel Gaussian Process Mutual Information algorithm (GP-MI), which significantly improves further these upper bounds for the cumulative regret. We confirm the efficiency of this algorithm on synthetic and real tasks against the natural competitor, GP-UCB, and also the Expected Improvement heuristic.