Deterministic Global Optimization of the Acquisition Function in Bayesian Optimization: To Do or Not To Do?

• URL: http://arxiv.org/abs/2503.03625v1
• Date: Wed, 05 Mar 2025 16:05:26 GMT
• Title: Deterministic Global Optimization of the Acquisition Function in Bayesian Optimization: To Do or Not To Do?
• Authors: Anastasia Georgiou, Daniel Jungen, Luise Kaven, Verena Hunstig, Constantine Frangakis, Ioannis Kevrekidis, Alexander Mitsos,
• Abstract summary: We investigate the advantages and disadvantages of using a deterministic global solver (MAiNGO) compared to conventional local and global solvers.<n>For CPU efficiency, we set a time limit for MAiNGO, taking the best point as optimal.
• Score: 36.814181034608666
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Bayesian Optimization (BO) with Gaussian Processes relies on optimizing an acquisition function to determine sampling. We investigate the advantages and disadvantages of using a deterministic global solver (MAiNGO) compared to conventional local and stochastic global solvers (L-BFGS-B and multi-start, respectively) for the optimization of the acquisition function. For CPU efficiency, we set a time limit for MAiNGO, taking the best point as optimal. We perform repeated numerical experiments, initially using the Muller-Brown potential as a benchmark function, utilizing the lower confidence bound acquisition function; we further validate our findings with three alternative benchmark functions. Statistical analysis reveals that when the acquisition function is more exploitative (as opposed to exploratory), BO with MAiNGO converges in fewer iterations than with the local solvers. However, when the dataset lacks diversity, or when the acquisition function is overly exploitative, BO with MAiNGO, compared to the local solvers, is more likely to converge to a local rather than a global ly near-optimal solution of the black-box function. L-BFGS-B and multi-start mitigate this risk in BO by introducing stochasticity in the selection of the next sampling point, which enhances the exploration of uncharted regions in the search space and reduces dependence on acquisition function hyperparameters. Ultimately, suboptimal optimization of poorly chosen acquisition functions may be preferable to their optimal solution. When the acquisition function is more exploratory, BO with MAiNGO, multi-start, and L-BFGS-B achieve comparable probabilities of convergence to a globally near-optimal solution (although BO with MAiNGO may require more iterations to converge under these conditions).

Related papers

• Optimizing Posterior Samples for Bayesian Optimization via Rootfinding [2.94944680995069]
  We introduce an efficient global optimization strategy for posterior samples based on global rootfinding.<n>Remarkably, even with just one point from each set, the global optimum is discovered most of the time.<n>Our approach also improves the performance of other posterior sample-based acquisition functions, such as variants of entropy search.
  arXiv  Detail & Related papers  (2024-10-29T17:57:16Z)
• High-dimensional Bayesian Optimization via Covariance Matrix Adaptation Strategy [16.521207412129833]
  We propose a novel technique for defining the local regions using the Covariance Matrix Adaptation (CMA) strategy. Based on this search distribution, we then define the local regions consisting of data points with high probabilities of being the global optimum. Our approach serves as a meta-algorithm as it can incorporate existing black-box BOs, such as BO, TuRBO, and BAxUS, to find the global optimum.
  arXiv  Detail & Related papers  (2024-02-05T15:32:10Z)
• Poisson Process for Bayesian Optimization [126.51200593377739]
  We propose a ranking-based surrogate model based on the Poisson process and introduce an efficient BO framework, namely Poisson Process Bayesian Optimization (PoPBO) Compared to the classic GP-BO method, our PoPBO has lower costs and better robustness to noise, which is verified by abundant experiments.
  arXiv  Detail & Related papers  (2024-02-05T02:54:50Z)
• BOtied: Multi-objective Bayesian optimization with tied multivariate ranks [33.414682601242006]
  In this paper, we show a natural connection between non-dominated solutions and the extreme quantile of the joint cumulative distribution function. Motivated by this link, we propose the Pareto-compliant CDF indicator and the associated acquisition function, BOtied. Our experiments on a variety of synthetic and real-world problems demonstrate that BOtied outperforms state-of-the-art MOBO acquisition functions.
  arXiv  Detail & Related papers  (2023-06-01T04:50:06Z)
• A Bayesian Optimization Framework for Finding Local Optima in Expensive Multi-Modal Functions [18.570591025615453]
  This paper develops a multimodal BO framework to find a set of local/global solutions for expensive-to-evaluate multimodal objective functions. We analytically derive the joint distribution of the objective function and its first-order derivatives. We introduce variants of the well-known BO acquisition functions to the multimodal setting and demonstrate the performance of the proposed framework.
  arXiv  Detail & Related papers  (2022-10-13T00:10:13Z)
• Generalizing Bayesian Optimization with Decision-theoretic Entropies [102.82152945324381]
  We consider a generalization of Shannon entropy from work in statistical decision theory. We first show that special cases of this entropy lead to popular acquisition functions used in BO procedures. We then show how alternative choices for the loss yield a flexible family of acquisition functions.
  arXiv  Detail & Related papers  (2022-10-04T04:43:58Z)
• Optimizing Bayesian acquisition functions in Gaussian Processes [0.0]
  This paper analyzes different acquistion functions like Probability of Maximum Improvement and Expected Improvement. Along with the analysis of time taken, the paper also shows the importance of position of initial samples chosen.
  arXiv  Detail & Related papers  (2021-11-09T03:25:15Z)
• Bayesian Algorithm Execution: Estimating Computable Properties of Black-box Functions Using Mutual Information [78.78486761923855]
  In many real world problems, we want to infer some property of an expensive black-box function f, given a budget of T function evaluations. We present a procedure, InfoBAX, that sequentially chooses queries that maximize mutual information with respect to the algorithm's output. On these problems, InfoBAX uses up to 500 times fewer queries to f than required by the original algorithm.
  arXiv  Detail & Related papers  (2021-04-19T17:22:11Z)
• Global Optimization of Gaussian processes [52.77024349608834]
  We propose a reduced-space formulation with trained Gaussian processes trained on few data points. The approach also leads to significantly smaller and computationally cheaper sub solver for lower bounding. In total, we reduce time convergence by orders of orders of the proposed method.
  arXiv  Detail & Related papers  (2020-05-21T20:59:11Z)
• Incorporating Expert Prior in Bayesian Optimisation via Space Warping [54.412024556499254]
  In big search spaces the algorithm goes through several low function value regions before reaching the optimum of the function. One approach to subside this cold start phase is to use prior knowledge that can accelerate the optimisation. In this paper, we represent the prior knowledge about the function optimum through a prior distribution. The prior distribution is then used to warp the search space in such a way that space gets expanded around the high probability region of function optimum and shrinks around low probability region of optimum.
  arXiv  Detail & Related papers  (2020-03-27T06:18:49Z)
• Composition of kernel and acquisition functions for High Dimensional Bayesian Optimization [0.1749935196721634]
  We use the addition-ality of the objective function into mapping both the kernel and the acquisition function of the Bayesian Optimization. This ap-proach makes more efficient the learning/updating of the probabilistic surrogate model. Results are presented for real-life application, that is the control of pumps in urban water distribution systems.
  arXiv  Detail & Related papers  (2020-03-09T15:45:57Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.