Vanilla Bayesian Optimization Performs Great in High Dimensions
- URL: http://arxiv.org/abs/2402.02229v5
- Date: Thu, 12 Dec 2024 09:53:38 GMT
- Title: Vanilla Bayesian Optimization Performs Great in High Dimensions
- Authors: Carl Hvarfner, Erik Orm Hellsten, Luigi Nardi,
- Abstract summary: High-dimensional problems have long been considered the Achilles' heel of Bayesian optimization algorithms.
We show how existing algorithms address these degeneracies through the lens of lowering the model complexity.
- Score: 5.7574684256411786
- License:
- Abstract: High-dimensional problems have long been considered the Achilles' heel of Bayesian optimization algorithms. Spurred by the curse of dimensionality, a large collection of algorithms aim to make it more performant in this setting, commonly by imposing various simplifying assumptions on the objective. In this paper, we identify the degeneracies that make vanilla Bayesian optimization poorly suited to high-dimensional tasks, and further show how existing algorithms address these degeneracies through the lens of lowering the model complexity. Moreover, we propose an enhancement to the prior assumptions that are typical to vanilla Bayesian optimization algorithms, which reduces the complexity to manageable levels without imposing structural restrictions on the objective. Our modification - a simple scaling of the Gaussian process lengthscale prior with the dimensionality - reveals that standard Bayesian optimization works drastically better than previously thought in high dimensions, clearly outperforming existing state-of-the-art algorithms on multiple commonly considered real-world high-dimensional tasks.
Related papers
- Understanding High-Dimensional Bayesian Optimization [8.07879230384311]
Recent work reported that simple Bayesian optimization methods perform well for high-dimensional real-world tasks.
We identify fundamental challenges that arise in high-dimensional Bayesian optimization and explain why recent methods succeed.
We propose a simple variant of maximum likelihood estimation called MSR that leverages these findings to achieve state-of-the-art performance.
arXiv Detail & Related papers (2025-02-13T11:37:55Z) - Expected Coordinate Improvement for High-Dimensional Bayesian Optimization [0.0]
We propose the expected coordinate improvement (ECI) criterion for high-dimensional Bayesian optimization.
The proposed approach selects the coordinate with the highest ECI value to refine in each iteration and covers all the coordinates gradually by iterating over the coordinates.
Numerical experiments show that the proposed algorithm can achieve significantly better results than the standard BO algorithm and competitive results when compared with five state-of-the-art high-dimensional BOs.
arXiv Detail & Related papers (2024-04-18T05:48:15Z) - Scalable Bayesian optimization with high-dimensional outputs using
randomized prior networks [3.0468934705223774]
We propose a deep learning framework for BO and sequential decision making based on bootstrapped ensembles of neural architectures with randomized priors.
We show that the proposed framework can approximate functional relationships between design variables and quantities of interest, even in cases where the latter take values in high-dimensional vector spaces or even infinite-dimensional function spaces.
We test the proposed framework against state-of-the-art methods for BO and demonstrate superior performance across several challenging tasks with high-dimensional outputs.
arXiv Detail & Related papers (2023-02-14T18:55:21Z) - Adaptive Stochastic Optimisation of Nonconvex Composite Objectives [2.1700203922407493]
We propose and analyse a family of generalised composite mirror descent algorithms.
With adaptive step sizes, the proposed algorithms converge without requiring prior knowledge of the problem.
We exploit the low-dimensional structure of the decision sets for high-dimensional problems.
arXiv Detail & Related papers (2022-11-21T18:31:43Z) - High dimensional Bayesian Optimization Algorithm for Complex System in
Time Series [1.9371782627708491]
This paper presents a novel high dimensional Bayesian optimization algorithm.
Based on the time-dependent or dimension-dependent characteristics of the model, the proposed algorithm can reduce the dimension evenly.
To increase the final accuracy of the optimal solution, the proposed algorithm adds a local search based on a series of Adam-based steps at the final stage.
arXiv Detail & Related papers (2021-08-04T21:21:17Z) - Unified Convergence Analysis for Adaptive Optimization with Moving Average Estimator [75.05106948314956]
We show that an increasing large momentum parameter for the first-order moment is sufficient for adaptive scaling.
We also give insights for increasing the momentum in a stagewise manner in accordance with stagewise decreasing step size.
arXiv Detail & Related papers (2021-04-30T08:50:24Z) - Sub-linear Regret Bounds for Bayesian Optimisation in Unknown Search
Spaces [63.22864716473051]
We propose a novel BO algorithm which expands (and shifts) the search space over iterations.
We show theoretically that for both our algorithms, the cumulative regret grows at sub-linear rates.
arXiv Detail & Related papers (2020-09-05T14:24:40Z) - Automatically Learning Compact Quality-aware Surrogates for Optimization
Problems [55.94450542785096]
Solving optimization problems with unknown parameters requires learning a predictive model to predict the values of the unknown parameters and then solving the problem using these values.
Recent work has shown that including the optimization problem as a layer in a complex training model pipeline results in predictions of iteration of unobserved decision making.
We show that we can improve solution quality by learning a low-dimensional surrogate model of a large optimization problem.
arXiv Detail & Related papers (2020-06-18T19:11:54Z) - Convergence of adaptive algorithms for weakly convex constrained
optimization [59.36386973876765]
We prove the $mathcaltilde O(t-1/4)$ rate of convergence for the norm of the gradient of Moreau envelope.
Our analysis works with mini-batch size of $1$, constant first and second order moment parameters, and possibly smooth optimization domains.
arXiv Detail & Related papers (2020-06-11T17:43:19Z) - Effective Dimension Adaptive Sketching Methods for Faster Regularized
Least-Squares Optimization [56.05635751529922]
We propose a new randomized algorithm for solving L2-regularized least-squares problems based on sketching.
We consider two of the most popular random embeddings, namely, Gaussian embeddings and the Subsampled Randomized Hadamard Transform (SRHT)
arXiv Detail & Related papers (2020-06-10T15:00:09Z) - Stochastic batch size for adaptive regularization in deep network
optimization [63.68104397173262]
We propose a first-order optimization algorithm incorporating adaptive regularization applicable to machine learning problems in deep learning framework.
We empirically demonstrate the effectiveness of our algorithm using an image classification task based on conventional network models applied to commonly used benchmark datasets.
arXiv Detail & Related papers (2020-04-14T07:54:53Z)
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.