Knowing The What But Not The Where in Bayesian Optimization
arXiv:1905.02685
Abstract
Bayesian optimization has demonstrated impressive success in finding the optimum input x* and output f* = f(x*) = max f(x) of a black-box function f. In some applications, however, the optimum output f* is known in advance and the goal is to find the corresponding optimum input x*. In this paper, we consider a new setting in BO in which the knowledge of the optimum output f* is available. Our goal is to exploit the knowledge about f* to search for the input x* efficiently. To achieve this goal, we first transform the Gaussian process surrogate using the information about the optimum output. Then, we propose two acquisition functions, called confidence bound minimization and expected regret minimization. We show that our approaches work intuitively and give quantitatively better performance against standard BO methods. We demonstrate real applications in tuning a deep reinforcement learning algorithm on the CartPole problem and XGBoost on Skin Segmentation dataset in which the optimum values are publicly available.
arXiv comment16 pages
References in corpus (14)
- Practical Bayesian Optimization of Machine Learning Algorithms
- A Tutorial on Bayesian Optimization of Expensive Cost Functions, with Application to Active User Modeling and Hierarchical Reinforcement Learning
- Scalable Bayesian Optimization Using Deep Neural Networks
- Predictive Entropy Search for Efficient Global Optimization of Black-box Functions
- A Tutorial on Bayesian Optimization
- Bayesian optimization for materials design
- Max-value Entropy Search for Efficient Bayesian Optimization
- Batched Large-scale Bayesian Optimization in High-dimensional Spaces
- Bayesian Optimization in AlphaGo
- BOCK : Bayesian Optimization with Cylindrical Kernels
- Sampling for Inference in Probabilistic Models with Fast Bayesian Quadrature
- Theoretical Analysis of Bayesian Optimisation with Unknown Gaussian Process Hyper-Parameters
- Fast Information-theoretic Bayesian Optimisation
- Nested Expectation Propagation for Gaussian Process Classification with a Multinomial Probit Likelihood