# Local Bayesian optimization via maximizing probability of descent

arXiv: https://arxiv.org/abs/2210.11662 · HTML: https://mlsanity.com/paper/2210.11662/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 31 references that are in the map.
- First posted on arXiv 21 Oct 2022.

## Builds on (most cited first, 11 of 11)

- [Scalable Global Optimization via Local Bayesian Optimization](https://mlsanity.com/paper/1910.01739/) (2019)
- [Batched Large-scale Bayesian Optimization in High-dimensional Spaces](https://mlsanity.com/paper/1706.01445/) (2017)
- [Learning Search Space Partition for Black-box Optimization using Monte Carlo Tree Search](https://mlsanity.com/paper/2007.00708/) (2020)
- [Think Global and Act Local: Bayesian Optimisation over High-Dimensional Categorical and Mixed Search Spaces](https://mlsanity.com/paper/2102.07188/) (2021)
- [Local policy search with Bayesian optimization](https://mlsanity.com/paper/2106.11899/) (2021)
- [Hybrid Batch Attacks: Finding Black-box Adversarial Examples with Limited Queries](https://mlsanity.com/paper/1908.07000/) (2019)
- [Probabilistic Line Searches for Stochastic Optimization](https://mlsanity.com/paper/1502.02846/) (2015)
- [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)
- [Optimizing High-Dimensional Physics Simulations via Composite Bayesian Optimization](https://mlsanity.com/paper/2111.14911/) (2021)
- [The Incremental Proximal Method: A Probabilistic Perspective](https://mlsanity.com/paper/1807.04594/) (2018)

## Built on by (most cited first, 30 of 30)

- [Vanilla Bayesian Optimization Performs Great in High Dimensions](https://mlsanity.com/paper/2402.02229/) (2024)
- [A survey and benchmark of high-dimensional Bayesian optimization of discrete sequences](https://mlsanity.com/paper/2406.04739/) (2024)
- [Self-Correcting Bayesian Optimization through Bayesian Active Learning](https://mlsanity.com/paper/2304.11005/) (2023)
- [The Behavior and Convergence of Local Bayesian Optimization](https://mlsanity.com/paper/2305.15572/) (2023)
- [We Still Don't Understand High-Dimensional Bayesian Optimization](https://mlsanity.com/paper/2512.00170/) (2025)
- [Minimizing UCB: a Better Local Search Strategy in Local Bayesian Optimization](https://mlsanity.com/paper/2405.15285/) (2024)
- [High-dimensional Bayesian Optimization via Covariance Matrix Adaptation Strategy](https://mlsanity.com/paper/2402.03104/) (2024)
- [User Preference Meets Pareto-Optimality in Multi-Objective Bayesian Optimization](https://mlsanity.com/paper/2502.06971/) (2025)
- [NeST-BO: Fast Local Bayesian Optimization via Newton-Step Targeting of Gradient and Hessian Information](https://mlsanity.com/paper/2510.05516/) (2025)
- [BayeSQP: Bayesian Optimization through Sequential Quadratic Programming](https://mlsanity.com/paper/2602.03232/) (2026)
- [CAGES: Cost-Aware Gradient Entropy Search for Efficient Local Multi-Fidelity Bayesian Optimization](https://mlsanity.com/paper/2405.07760/) (2024)
- [Covariance-Adaptive Sequential Black-box Optimization for Diffusion Targeted Generation](https://mlsanity.com/paper/2406.00812/) (2024)
- [Simulation-Aided Policy Tuning for Black-Box Robot Learning](https://mlsanity.com/paper/2411.14246/) (2024)
- [Safe Bayesian Optimization for the Control of High-Dimensional Embodied Systems](https://mlsanity.com/paper/2412.20350/) (2024)
- [Bayesian Optimisation Against Climate Change: Applications and Benchmarks](https://mlsanity.com/paper/2306.04343/) (2023)
- [Local Bayesian Optimization for Controller Tuning with Crash Constraints](https://mlsanity.com/paper/2411.16267/) (2024)
- [Augmented Bayesian Policy Search](https://mlsanity.com/paper/2407.04864/) (2024)
- [Sharpness-Aware Black-Box Optimization](https://mlsanity.com/paper/2410.12457/) (2024)
- [End-to-End Optimal Detector Design with Mutual Information Surrogates](https://mlsanity.com/paper/2503.14342/) (2025)
- [Bencher: Simple and Reproducible Benchmarking for Black-Box Optimization](https://mlsanity.com/paper/2505.21321/) (2025)
- [Enhancing Trust-Region Bayesian Optimization via Newton Methods](https://mlsanity.com/paper/2508.18423/) (2025)
- [Rethinking Trust Region Bayesian Optimization in High Dimensions](https://mlsanity.com/paper/2604.22967/) (2026)
- [Local Entropy Search over Descent Sequences for Bayesian Optimization](https://mlsanity.com/paper/2511.19241/) (2025)
- [Adaptive Candidate Point Thompson Sampling for High-Dimensional Bayesian Optimization](https://mlsanity.com/paper/2604.08891/) (2026)
- [Adaptive Replication Strategies in Trust-Region-Based Bayesian Optimization of Stochastic Functions](https://mlsanity.com/paper/2504.20527/) (2025)
- [Beyond Objective-Based Improvement: Stationarity-Aware Expected Improvement for Bayesian Optimization](https://mlsanity.com/paper/2601.21357/) (2026)
- [Local Constrained Bayesian Optimization](https://mlsanity.com/paper/2603.07965/) (2026)
- [Local Preferential Bayesian Optimization](https://mlsanity.com/paper/2606.02351/) (2026)
- [GRAPE: Gradient Refinement and Progress-Aware Exploitation for Query-Efficient High-Dimensional Bayesian Optimization](https://mlsanity.com/paper/2608.25116/) (2026)
- [Isotropic Gaussian Processes Improve Vanilla Bayesian Optimization in High Dimensions](https://mlsanity.com/paper/2610.05780/) (2026)

## Abstract (arXiv)

Local optimization presents a promising approach to expensive, high-dimensional black-box optimization by sidestepping the need to globally explore the search space. For objective functions whose gradient cannot be evaluated directly, Bayesian optimization offers one solution -- we construct a probabilistic model of the objective, design a policy to learn about the gradient at the current location, and use the resulting information to navigate the objective landscape. Previous work has realized this scheme by minimizing the variance in the estimate of the gradient, then moving in the direction of the expected gradient. In this paper, we re-examine and refine this approach. We demonstrate that, surprisingly, the expected value of the gradient is not always the direction maximizing the probability of descent, and in fact, these directions may be nearly orthogonal. This observation then inspires an elegant optimization scheme seeking to maximize the probability of descent while moving in the direction of most-probable descent. Experiments on both synthetic and real-world objectives show that our method outperforms previous realizations of this optimization scheme and is competitive against other, significantly more complicated baselines.