Bayesian Optimization in Linear Time

• URL: http://arxiv.org/abs/2605.00237v1
• Date: Thu, 30 Apr 2026 21:16:12 GMT
• Title: Bayesian Optimization in Linear Time
• Abstract summary: We show that our method achieves superior optimization performance in all tests.<n>We adapt both the modeling and acquisitive aspects of standard Bayesian optimization to work harmoniously with the partitioning scheme.
• Score: 1.6500749121196987
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Bayesian optimization is a sequential method for minimizing objective functions that are expensive to evaluate and about which few assumptions can be made. By using all gathered data to train a Gaussian process model for the function and adaptively employing a mixture of global exploration and local exploitation, this method has been used for optimization in many fields including machine learning, automotive engineering and reinforcement learning. However, the standard method suffers from two problems: 1) with cubic computational complexity in the training-set size it eventually becomes computationally infeasible to train the model, and 2) globally modeling the objective function is not necessarily optimal given the local nature of minimization. Using flexible and recursive binary partitioning of the search space, we adapt both the modeling and acquisitive aspects of standard Bayesian optimization to work harmoniously with the partitioning scheme, thereby ameliorating both standard shortcomings. We compare our method against a commonly used Bayesian optimization library on seven challenging test functions, ranging in dimensionality from $6$ to $124$, and show that our method achieves superior optimization performance in all tests. In addition our method has linear computational complexity.

Related papers

• Divide and Learn: Multi-Objective Combinatorial Optimization at Scale [41.78439888126577]
  Multi-objective optimization seeks solutions over exponentially large discrete spaces.<n>We reformulate it as an online learning problem over a decomposed decision space, solving position-wise bandit subproblems.<n>On standard benchmarks, our method achieves 80--98% of specialized solvers performance.
  arXiv  Detail & Related papers  (2026-02-11T20:29:35Z)
• Make Optimization Once and for All with Fine-grained Guidance [78.14885351827232]
  Learning to Optimize (L2O) enhances optimization efficiency with integrated neural networks.<n>L2O paradigms achieve great outcomes, e.g., refitting, generating unseen solutions iteratively or directly.<n>Our analyses explore general framework for learning optimization, called Diff-L2O, focusing on augmenting solutions from a wider view.
  arXiv  Detail & Related papers  (2025-03-14T14:48:12Z)
• Contextual Stochastic Bilevel Optimization [50.36775806399861]
  We introduce contextual bilevel optimization (CSBO) -- a bilevel optimization framework with the lower-level problem minimizing an expectation on some contextual information and the upper-level variable. It is important for applications such as meta-learning, personalized learning, end-to-end learning, and Wasserstein distributionally robustly optimization with side information (WDRO-SI)
  arXiv  Detail & Related papers  (2023-10-27T23:24:37Z)
• Accelerating Cutting-Plane Algorithms via Reinforcement Learning Surrogates [49.84541884653309]
  A current standard approach to solving convex discrete optimization problems is the use of cutting-plane algorithms. Despite the existence of a number of general-purpose cut-generating algorithms, large-scale discrete optimization problems continue to suffer from intractability. We propose a method for accelerating cutting-plane algorithms via reinforcement learning.
  arXiv  Detail & Related papers  (2023-07-17T20:11:56Z)
• Symmetric Replay Training: Enhancing Sample Efficiency in Deep Reinforcement Learning for Combinatorial Optimization [42.92248233465095]
  We propose a simple but effective method, called symmetric replay training (SRT), which can be easily integrated into various Deep reinforcement learning (DRL) methods. Our method leverages high-reward samples to encourage exploration of symmetric regions without additional online interactions - free. Experimental results demonstrate the consistent improvement of our method in sample efficiency across diverse DRL methods applied to real-world tasks.
  arXiv  Detail & Related papers  (2023-06-02T05:34:01Z)
• Bayesian Optimization over Permutation Spaces [30.650753803587794]
  We propose and evaluate two algorithms for BO over Permutation Spaces (BOPS) We theoretically analyze the performance of BOPS-T to show that their regret grows sub-linearly. Our experiments on multiple synthetic and real-world benchmarks show that both BOPS-T and BOPS-H perform better than the state-of-the-art BO algorithm for spaces.
  arXiv  Detail & Related papers  (2021-12-02T08:20:50Z)
• Combinatorial Bayesian Optimization with Random Mapping Functions to Convex Polytopes [43.19936635161588]
  We present a method for Bayesian optimization in a space which can operate well in a large space. Our algorithm shows satisfactory performance compared to existing methods.
  arXiv  Detail & Related papers  (2020-11-26T02:22:41Z)
• 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)
• Learning to Guide Random Search [111.71167792453473]
  We consider derivative-free optimization of a high-dimensional function that lies on a latent low-dimensional manifold. We develop an online learning approach that learns this manifold while performing the optimization. We empirically evaluate the method on continuous optimization benchmarks and high-dimensional continuous control problems.
  arXiv  Detail & Related papers  (2020-04-25T19:21:14Z)
• Learning to be Global Optimizer [28.88646928299302]
  We learn an optimal network and escaping capability algorithm for some benchmark functions. We show that the learned algorithm significantly outperforms some well-known classical optimization algorithms.
  arXiv  Detail & Related papers  (2020-03-10T03:46:25Z)
• Self-Directed Online Machine Learning for Topology Optimization [58.920693413667216]
  Self-directed Online Learning Optimization integrates Deep Neural Network (DNN) with Finite Element Method (FEM) calculations. Our algorithm was tested by four types of problems including compliance minimization, fluid-structure optimization, heat transfer enhancement and truss optimization. It reduced the computational time by 2 5 orders of magnitude compared with directly using methods, and outperformed all state-of-the-art algorithms tested in our experiments.
  arXiv  Detail & Related papers  (2020-02-04T20:00:28Z)

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.