# LAGO: A Local-Global Optimization Framework Combining Trust Region Methods and Bayesian Optimization

arXiv: https://arxiv.org/abs/2603.02970 · HTML: https://mlsanity.com/paper/2603.02970/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 46 references that are in the map.
- First posted on arXiv 3 Mar 2026.

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

- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [A Tutorial on Bayesian Optimization](https://mlsanity.com/paper/1807.02811/) (2018)
- [Scalable Global Optimization via Local Bayesian Optimization](https://mlsanity.com/paper/1910.01739/) (2019)
- [Bayesian Optimization with Safety Constraints: Safe and Automatic Parameter Tuning in Robotics](https://mlsanity.com/paper/1602.04450/) (2016)
- [A survey on high-dimensional Gaussian process modeling with application to Bayesian optimization](https://mlsanity.com/paper/2111.05040/) (2021)
- [Bayesian Optimization with Gradients](https://mlsanity.com/paper/1703.04389/) (2017)
- [Improving the Expected Improvement Algorithm](https://mlsanity.com/paper/1705.10033/) (2017)
- [Convergence Guarantees for Gaussian Process Means With Misspecified Likelihoods and Smoothness](https://mlsanity.com/paper/2001.10818/) (2020)
- [TREGO: a Trust-Region Framework for Efficient Global Optimization](https://mlsanity.com/paper/2101.06808/) (2021)
- [Optimization, fast and slow: optimally switching between local and Bayesian optimization](https://mlsanity.com/paper/1805.08610/) (2018)
- [Understanding High-Dimensional Bayesian Optimization](https://mlsanity.com/paper/2502.09198/) (2025)
- [Practical Bayesian Optimization for Model Fitting with Bayesian Adaptive Direct Search](https://mlsanity.com/paper/1705.04405/) (2017)
- [Trieste: Efficiently Exploring The Depths of Black-box Functions with TensorFlow](https://mlsanity.com/paper/2302.08436/) (2023)
- [BayeSQP: Bayesian Optimization through Sequential Quadratic Programming](https://mlsanity.com/paper/2602.03232/) (2026)
- [PyBADS: Fast and robust black-box optimization in Python](https://mlsanity.com/paper/2306.15576/) (2023)
- [LABCAT: Locally adaptive Bayesian optimization using principal-component-aligned trust regions](https://mlsanity.com/paper/2311.11328/) (2023)
- [Enhancing Trust-Region Bayesian Optimization via Newton Methods](https://mlsanity.com/paper/2508.18423/) (2025)

## Abstract (arXiv)

We introduce LAGO, a LocAl-Global Optimization framework coupling Bayesian Optimization (BO) and gradient-based trust region local refinement through an adaptive competition mechanism for smooth expensive-to-evaluate objective functions with available gradients. At each iteration, global and local optimization strategies independently propose candidate points, and the next evaluation is selected based on predicted improvement. LAGO separates global exploration from local refinement at the proposal level: the BO acquisition function is optimized outside the active trust region, while local candidates are proposed within the trust region. Points in the vicinity of the accepted local step are incorporated in the global GP dataset only when satisfying a lengthscale-based minimum-distance criterion, hence reducing the risk of numerical instability during local exploitation. LAGO enhances BO with efficient local refinement when reaching promising regions, and reverts to exploratory behavior when local steps are not competitive.