# Nonmyopic Global Optimisation via Approximate Dynamic Programming

arXiv: https://arxiv.org/abs/2412.04882 · HTML: https://mlsanity.com/paper/2412.04882/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 60 references that are in the map.
- First posted on arXiv 6 Dec 2024.

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

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Max-value Entropy Search for Efficient Bayesian Optimization](https://mlsanity.com/paper/1703.01968/) (2017)
- [A Literature Survey of Benchmark Functions For Global Optimization Problems](https://mlsanity.com/paper/1308.4008/) (2013)
- [Efficient Nonmyopic Bayesian Optimization via One-Shot Multi-Step Trees](https://mlsanity.com/paper/2006.15779/) (2020)
- [GLASSES: Relieving The Myopia Of Bayesian Optimisation](https://mlsanity.com/paper/1510.06299/) (2015)
- [BINOCULARS for Efficient, Nonmyopic Sequential Experimental Design](https://mlsanity.com/paper/1909.04568/) (2019)
- [The Scenario Approach for Stochastic Model Predictive Control with Bounds on Closed-Loop Constraint Violations](https://mlsanity.com/paper/1307.5640/) (2013)
- [Global Optimization of Objective Functions Represented by ReLU Networks](https://mlsanity.com/paper/2010.03258/) (2020)
- [Why Non-myopic Bayesian Optimization is Promising and How Far Should We Look-ahead? A Study via Rollout](https://mlsanity.com/paper/1911.01004/) (2019)
- [Efficient Rollout Strategies for Bayesian Optimization](https://mlsanity.com/paper/2002.10539/) (2020)
- [A Nonmyopic Approach to Cost-Constrained Bayesian Optimization](https://mlsanity.com/paper/2106.06079/) (2021)
- [Global optimization via inverse distance weighting and radial basis functions](https://mlsanity.com/paper/1906.06498/) (2019)
- [A Data-Driven Automatic Tuning Method for MPC under Uncertainty using Constrained Bayesian Optimization](https://mlsanity.com/paper/2011.11841/) (2020)
- [Active Learning for Regression by Inverse Distance Weighting](https://mlsanity.com/paper/2204.07177/) (2022)
- [Learning safety in model-based Reinforcement Learning using MPC and Gaussian Processes](https://mlsanity.com/paper/2211.01860/) (2022)
- [Rollout Algorithms and Approximate Dynamic Programming for Bayesian Optimization and Sequential Estimation](https://mlsanity.com/paper/2212.07998/) (2022)
- [Suboptimality analysis of receding horizon quadratic control with unknown linear systems and its applications in learning-based control](https://mlsanity.com/paper/2301.07876/) (2023)

## Abstract (arXiv)

Global optimisation to optimise expensive-to-evaluate black-box functions without gradient information. Bayesian optimisation, one of the most well-known techniques, typically employs Gaussian processes as surrogate models, leveraging their probabilistic nature to balance exploration and exploitation. However, these processes become computationally prohibitive in high-dimensional spaces. Recent alternatives, based on inverse distance weighting (IDW) and radial basis functions (RBFs), offer competitive, computationally lighter solutions. Despite their efficiency, both traditional global and Bayesian optimisation strategies suffer from the myopic nature of their acquisition functions, which focus on immediate improvement neglecting future implications of the sequential decision making process. Nonmyopic acquisition functions devised for the Bayesian setting have shown promise in improving long-term performance. Yet, their combination with deterministic surrogate models remains unexplored. In this work, we introduce novel nonmyopic acquisition strategies tailored to IDW and RBF based on approximate dynamic programming paradigms, including rollout and multi-step scenario-based optimisation schemes, to enable lookahead acquisition. These methods optimise a sequence of query points over a horizon by predicting the evolution of the surrogate model, inherently managing the exploration-exploitation trade-off via optimisation techniques. The proposed approach represents a significant advance in extending nonmyopic acquisition principles, previously confined to Bayesian optimisation, to deterministic models. Empirical results on synthetic and hyperparameter tuning benchmark problems, a constrained problem, as well as on a data-driven predictive control application, demonstrate that these nonmyopic methods outperform conventional myopic approaches, leading to faster and more robust convergence.