Relaxing the Additivity Constraints in Decentralized No-Regret High-Dimensional Bayesian Optimization

• URL: http://arxiv.org/abs/2305.19838v4
• Date: Thu, 8 Feb 2024 16:47:35 GMT
• Title: Relaxing the Additivity Constraints in Decentralized No-Regret High-Dimensional Bayesian Optimization
• Authors: Anthony Bardou, Patrick Thiran and Thomas Begin
• Abstract summary: We relax the restrictive assumptions on the additive structure $f$ without weakening the guarantees of the acquisition function. We propose an optimal decentralized BO algorithm that achieves very competitive performance against state-of-the-art BO algorithms.
• Score: 5.316089560623732
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Bayesian Optimization (BO) is typically used to optimize an unknown function $f$ that is noisy and costly to evaluate, by exploiting an acquisition function that must be maximized at each optimization step. Even if provably asymptotically optimal BO algorithms are efficient at optimizing low-dimensional functions, scaling them to high-dimensional spaces remains an open problem, often tackled by assuming an additive structure for $f$. By doing so, BO algorithms typically introduce additional restrictive assumptions on the additive structure that reduce their applicability domain. This paper contains two main contributions: (i) we relax the restrictive assumptions on the additive structure of $f$ without weakening the maximization guarantees of the acquisition function, and (ii) we address the over-exploration problem for decentralized BO algorithms. To these ends, we propose DuMBO, an asymptotically optimal decentralized BO algorithm that achieves very competitive performance against state-of-the-art BO algorithms, especially when the additive structure of $f$ comprises high-dimensional factors.

Related papers

• Dimensionality Reduction Techniques for Global Bayesian Optimisation [1.433758865948252]
  We explore Latent Space Bayesian optimisation, that applies dimensionality reduction to perform BO in a reduced-dimensional subspace. We employ Variational Autoencoders (VAEs) to manage more complex data structures and general DR tasks. We suggest a few key corrections in their implementation, originally designed for tasks such as molecule generation, and reformulate the algorithm for broader optimisation purposes.
  arXiv  Detail & Related papers  (2024-12-12T11:27:27Z)
• Cost-Sensitive Multi-Fidelity Bayesian Optimization with Transfer of Learning Curve Extrapolation [55.75188191403343]
  We introduce utility, which is a function predefined by each user and describes the trade-off between cost and performance of BO. We validate our algorithm on various LC datasets and found it outperform all the previous multi-fidelity BO and transfer-BO baselines we consider.
  arXiv  Detail & Related papers  (2024-05-28T07:38:39Z)
• LABCAT: Locally adaptive Bayesian optimization using principal-component-aligned trust regions [0.0]
  We propose the LABCAT algorithm, which extends trust-region-based BO. We show that the algorithm outperforms several state-of-the-art BO and other black-box optimization algorithms.
  arXiv  Detail & Related papers  (2023-11-19T13:56:24Z)
• Fast Computation of Optimal Transport via Entropy-Regularized Extragradient Methods [75.34939761152587]
  Efficient computation of the optimal transport distance between two distributions serves as an algorithm that empowers various applications. This paper develops a scalable first-order optimization-based method that computes optimal transport to within $varepsilon$ additive accuracy.
  arXiv  Detail & Related papers  (2023-01-30T15:46:39Z)
• Model-based Causal Bayesian Optimization [78.120734120667]
  We propose model-based causal Bayesian optimization (MCBO) MCBO learns a full system model instead of only modeling intervention-reward pairs. Unlike in standard Bayesian optimization, our acquisition function cannot be evaluated in closed form.
  arXiv  Detail & Related papers  (2022-11-18T14:28:21Z)
• 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)
• A General Recipe for Likelihood-free Bayesian Optimization [115.82591413062546]
  We propose likelihood-free BO (LFBO) to extend BO to a broader class of models and utilities. LFBO directly models the acquisition function without having to separately perform inference with a probabilistic surrogate model. We show that computing the acquisition function in LFBO can be reduced to optimizing a weighted classification problem.
  arXiv  Detail & Related papers  (2022-06-27T03:55:27Z)
• Ada-BKB: Scalable Gaussian Process Optimization on Continuous Domain by Adaptive Discretization [21.859940486704264]
  An algorithm such as GPUCB has prohibitive computational complexity. A norere algorithm for functions corroborates the real problem of continuous optimization.
  arXiv  Detail & Related papers  (2021-06-16T07:55:45Z)
• Bayesian Optimistic Optimisation with Exponentially Decaying Regret [58.02542541410322]
  The current practical BO algorithms have regret bounds ranging from $mathcalO(fraclogNsqrtN)$ to $mathcal O(e-sqrtN)$, where $N$ is the number of evaluations. This paper explores the possibility of improving the regret bound in the noiseless setting by intertwining concepts from BO and tree-based optimistic optimisation. We propose the BOO algorithm, a first practical approach which can achieve an exponential regret bound with order $mathcal O(N-sqrt
  arXiv  Detail & Related papers  (2021-05-10T13:07:44Z)
• Additive Tree-Structured Conditional Parameter Spaces in Bayesian Optimization: A Novel Covariance Function and a Fast Implementation [34.89735938765757]
  We generalize the additive assumption to tree-structured functions, showing improved sample-efficiency, wider applicability and greater flexibility. By incorporating the structure information of parameter spaces and the additive assumption in the BO loop, we develop a parallel algorithm to optimize the acquisition function. We demonstrate our method on an optimization benchmark function, on pruning pre-trained VGG16 and Res50 models as well as on searching activation functions of ResNet20.
  arXiv  Detail & Related papers  (2020-10-06T16:08:58Z)
• Additive Tree-Structured Covariance Function for Conditional Parameter Spaces in Bayesian Optimization [34.89735938765757]
  We generalize the additive assumption to tree-structured functions. By incorporating the structure information of parameter spaces and the additive assumption in the BO loop, we develop a parallel algorithm to optimize the acquisition function.
  arXiv  Detail & Related papers  (2020-06-21T11:21:55Z)

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.