Maximizing acquisition functions for Bayesian optimization

Abstract

Bayesian optimization is a sample-efficient approach to global optimization that relies on theoretically motivated value heuristics (acquisition functions) to guide its search process. Fully maximizing acquisition functions produces the Bayes' decision rule, but this ideal is difficult to achieve since these functions are frequently non-trivial to optimize. This statement is especially true when evaluating queries in parallel, where acquisition functions are routinely non-convex, high-dimensional, and intractable. We first show that acquisition functions estimated via Monte Carlo integration are consistently amenable to gradient-based optimization. Subsequently, we identify a common family of acquisition functions, including EI and UCB, whose properties not only facilitate but justify use of greedy approaches for their maximization.

arXiv commentProceedings of the Thirty-second Conference on Neural Information Processing Systems, 2018

Cited by in corpus (24)

• Differentiable Expected Hypervolume Improvement for Parallel Multi-Objective Bayesian Optimization
• Monte Carlo Gradient Estimation in Machine Learning
• Parallel Bayesian Optimization of Multiple Noisy Objectives with Expected Hypervolume Improvement
• Cost-aware Bayesian Optimization
• Is novelty predictable?
• Are we Forgetting about Compositional Optimisers in Bayesian Optimisation?
• On Local Optimizers of Acquisition Functions in Bayesian Optimization
• Efficiently Sampling Functions from Gaussian Process Posteriors
• Data acquisition and image processing for solar irradiance forecasting
• Better call Surrogates: A hybrid Evolutionary Algorithm for Hyperparameter optimization
• Batch simulations and uncertainty quantification in Gaussian process surrogate approximate Bayesian computation
• Bayesian Optimization with High-Dimensional Outputs
• Achieving Robustness to Aleatoric Uncertainty with Heteroscedastic Bayesian Optimisation
• Multi-Step Budgeted Bayesian Optimization with Unknown Evaluation Costs
• Pathwise Conditioning of Gaussian Processes
• Practical Transfer Learning for Bayesian Optimization
• Efficient Nonmyopic Bayesian Optimization via One-Shot Multi-Step Trees
• A portfolio approach to massively parallel Bayesian optimization
• Optimizing Discrete Spaces via Expensive Evaluations: A Learning to Search Framework
• Sequential- and Parallel- Constrained Max-value Entropy Search via Information Lower Bound
• Bayesian Variational Optimization for Combinatorial Spaces
• LinEasyBO: Scalable Bayesian Optimization Approach for Analog Circuit Synthesis via One-Dimensional Subspaces
• GaussED: A Probabilistic Programming Language for Sequential Experimental Design
• Surrogate Assisted Evolutionary Algorithm for Medium Scale Expensive Multi-Objective Optimisation Problems