BORE: Bayesian Optimization by Density-Ratio Estimation

• URL: http://arxiv.org/abs/2102.09009v1
• Date: Wed, 17 Feb 2021 20:04:11 GMT
• Title: BORE: Bayesian Optimization by Density-Ratio Estimation
• Authors: Louis C. Tiao, Aaron Klein, Matthias Seeger, Edwin V. Bonilla, Cedric Archambeau, Fabio Ramos
• Abstract summary: We cast the expected improvement (EI) function as a binary classification problem, building on the link between class-probability estimation and density-ratio estimation. This reformulation provides numerous advantages, not least in terms of versatility, and scalability.
• Score: 34.22533785573784
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Bayesian optimization (BO) is among the most effective and widely-used blackbox optimization methods. BO proposes solutions according to an explore-exploit trade-off criterion encoded in an acquisition function, many of which are computed from the posterior predictive of a probabilistic surrogate model. Prevalent among these is the expected improvement (EI) function. The need to ensure analytical tractability of the predictive often poses limitations that can hinder the efficiency and applicability of BO. In this paper, we cast the computation of EI as a binary classification problem, building on the link between class-probability estimation and density-ratio estimation, and the lesser-known link between density-ratios and EI. By circumventing the tractability constraints, this reformulation provides numerous advantages, not least in terms of expressiveness, versatility, and scalability.

Related papers

• 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)
• Simulation Based Bayesian Optimization [0.6526824510982799]
  This paper introduces Simulation Based Bayesian Optimization (SBBO) as a novel approach to optimizing acquisition functions. SBBO allows the use of surrogate models tailored for spaces with discrete variables. We demonstrate empirically the effectiveness of SBBO method using various choices of surrogate models.
  arXiv  Detail & Related papers  (2024-01-19T16:56:11Z)
• Stochastic Bayesian Optimization with Unknown Continuous Context Distribution via Kernel Density Estimation [28.413085548038932]
  We propose two algorithms that employ kernel density estimation to learn the probability density function (PDF) of continuous context variable online. Theoretical results demonstrate that both algorithms have sub-linear Bayesian cumulative regret on the expectation objective.
  arXiv  Detail & Related papers  (2023-12-16T11:32:28Z)
• Equation Discovery with Bayesian Spike-and-Slab Priors and Efficient Kernels [57.46832672991433]
  We propose a novel equation discovery method based on Kernel learning and BAyesian Spike-and-Slab priors (KBASS) We use kernel regression to estimate the target function, which is flexible, expressive, and more robust to data sparsity and noises. We develop an expectation-propagation expectation-maximization algorithm for efficient posterior inference and function estimation.
  arXiv  Detail & Related papers  (2023-10-09T03:55:09Z)
• Density Ratio Estimation-based Bayesian Optimization with Semi-Supervised Learning [5.346298077607419]
  We propose density ratio estimation-based Bayesian optimization with semi-supervised learning to solve this challenge. We show the empirical results of our methods and several baseline methods in two distinct scenarios with unlabeled point sampling and a fixed-size pool.
  arXiv  Detail & Related papers  (2023-05-24T23:01:56Z)
• 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)
• Batch Bayesian optimisation via density-ratio estimation with guarantees [26.052368583196426]
  We present a theoretical analysis of BORE's regret and an extension of the algorithm with improved uncertainty estimates. We also show that BORE can be naturally extended to a batch optimisation setting by recasting the problem as approximate Bayesian inference.
  arXiv  Detail & Related papers  (2022-09-22T00:42:18Z)
• Tree ensemble kernels for Bayesian optimization with known constraints over mixed-feature spaces [54.58348769621782]
  Tree ensembles can be well-suited for black-box optimization tasks such as algorithm tuning and neural architecture search. Two well-known challenges in using tree ensembles for black-box optimization are (i) effectively quantifying model uncertainty for exploration and (ii) optimizing over the piece-wise constant acquisition function. Our framework performs as well as state-of-the-art methods for unconstrained black-box optimization over continuous/discrete features and outperforms competing methods for problems combining mixed-variable feature spaces and known input constraints.
  arXiv  Detail & Related papers  (2022-07-02T16:59:37Z)
• 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)
• Approximate Bayesian Optimisation for Neural Networks [6.921210544516486]
  A body of work has been done to automate machine learning algorithm to highlight the importance of model choice. The necessity to solve the analytical tractability and the computational feasibility in a idealistic fashion enables to ensure the efficiency and the applicability.
  arXiv  Detail & Related papers  (2021-08-27T19:03:32Z)

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.