Bayesian Optimisation for Constrained Problems

• URL: http://arxiv.org/abs/2105.13245v1
• Date: Thu, 27 May 2021 15:43:09 GMT
• Title: Bayesian Optimisation for Constrained Problems
• Authors: Juan Ungredda and Juergen Branke
• Abstract summary: We propose a novel variant of the well-known Knowledge Gradient acquisition function that allows it to handle constraints. We empirically compare the new algorithm with four other state-of-the-art constrained Bayesian optimisation algorithms and demonstrate its superior performance.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Many real-world optimisation problems such as hyperparameter tuning in machine learning or simulation-based optimisation can be formulated as expensive-to-evaluate black-box functions. A popular approach to tackle such problems is Bayesian optimisation (BO), which builds a response surface model based on the data collected so far, and uses the mean and uncertainty predicted by the model to decide what information to collect next. In this paper, we propose a novel variant of the well-known Knowledge Gradient acquisition function that allows it to handle constraints. We empirically compare the new algorithm with four other state-of-the-art constrained Bayesian optimisation algorithms and demonstrate its superior performance. We also prove theoretical convergence in the infinite budget limit.

Related papers

• Learning Joint Models of Prediction and Optimization [56.04498536842065]
  Predict-Then-Then framework uses machine learning models to predict unknown parameters of an optimization problem from features before solving. This paper proposes an alternative method, in which optimal solutions are learned directly from the observable features by joint predictive models.
  arXiv  Detail & Related papers  (2024-09-07T19:52:14Z)
• End-to-End Learning for Fair Multiobjective Optimization Under Uncertainty [55.04219793298687]
  The Predict-Then-Forecast (PtO) paradigm in machine learning aims to maximize downstream decision quality. This paper extends the PtO methodology to optimization problems with nondifferentiable Ordered Weighted Averaging (OWA) objectives. It shows how optimization of OWA functions can be effectively integrated with parametric prediction for fair and robust optimization under uncertainty.
  arXiv  Detail & Related papers  (2024-02-12T16:33:35Z)
• Pseudo-Bayesian Optimization [7.556071491014536]
  We study an axiomatic framework that elicits the minimal requirements to guarantee black-box optimization convergence. We show how using simple local regression, and a suitable "randomized prior" construction to quantify uncertainty, not only guarantees convergence but also consistently outperforms state-of-the-art benchmarks.
  arXiv  Detail & Related papers  (2023-10-15T07:55:28Z)
• No-Regret Constrained Bayesian Optimization of Noisy and Expensive Hybrid Models using Differentiable Quantile Function Approximations [0.0]
  Constrained Upper Quantile Bound (CUQB) is a conceptually simple, deterministic approach that avoids constraint approximations. We show that CUQB significantly outperforms traditional Bayesian optimization in both constrained and unconstrained cases.
  arXiv  Detail & Related papers  (2023-05-05T19:57:36Z)
• Optimizing Pessimism in Dynamic Treatment Regimes: A Bayesian Learning Approach [6.7826352751791985]
  We propose a novel pessimism-based Bayesian learning method for optimal dynamic treatment regimes in the offline setting. We integrate the pessimism principle with Thompson sampling and Bayesian machine learning for optimizing the degree of pessimism. We develop the computational algorithm based on variational inference, which is highly efficient and scalable.
  arXiv  Detail & Related papers  (2022-10-26T02:14:10Z)
• 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)
• 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)
• 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)
• Adaptive Sampling of Pareto Frontiers with Binary Constraints Using Regression and Classification [0.0]
  We present a novel adaptive optimization algorithm for black-box multi-objective optimization problems with binary constraints. Our method is based on probabilistic regression and classification models, which act as a surrogate for the optimization goals. We also present a novel ellipsoid truncation method to speed up the expected hypervolume calculation.
  arXiv  Detail & Related papers  (2020-08-27T09:15:02Z)
• 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)
• Scalable Constrained Bayesian Optimization [10.820024633762596]
  The global optimization of a high-dimensional black-box function under black-box constraints is a pervasive task in machine learning, control, and the scientific community. We propose the scalable constrained Bayesian optimization (SCBO) algorithm that overcomes the above challenges and pushes the state-the-art.
  arXiv  Detail & Related papers  (2020-02-20T01:48:46Z)

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.