The reparameterization trick for acquisition functions

by   James T. Wilson, et al.
University of Freiburg
Imperial College London

Bayesian optimization is a sample-efficient approach to solving global optimization problems. Along with a surrogate model, this approach relies on theoretically motivated value heuristics (acquisition functions) to guide the search process. Maximizing acquisition functions yields the best performance; unfortunately, this ideal is difficult to achieve since optimizing acquisition functions per se is frequently non-trivial. This statement is especially true in the parallel setting, where acquisition functions are routinely non-convex, high-dimensional, and intractable. Here, we demonstrate how many popular acquisition functions can be formulated as Gaussian integrals amenable to the reparameterization trick and, ensuingly, gradient-based optimization. Further, we use this reparameterized representation to derive an efficient Monte Carlo estimator for the upper confidence bound acquisition function in the context of parallel selection.


Maximizing acquisition functions for Bayesian optimization

Bayesian optimization is a sample-efficient approach to global optimizat...

Efficient Rollout Strategies for Bayesian Optimization

Bayesian optimization (BO) is a class of sample-efficient global optimiz...

Bayesian Optimization for Min Max Optimization

A solution that is only reliable under favourable conditions is hardly a...

Optimizing Bayesian acquisition functions in Gaussian Processes

Bayesian Optimization is an effective method for searching the global ma...

Expected Improvement versus Predicted Value in Surrogate-Based Optimization

Surrogate-based optimization relies on so-called infill criteria (acquis...

Enhancing High-dimensional Bayesian Optimization by Optimizing the Acquisition Function Maximizer Initialization

Bayesian optimization (BO) is widely used to optimize black-box function...

Parallelized Acquisition for Active Learning using Monte Carlo Sampling

Bayesian inference remains one of the most important tool-kits for any s...

Please sign up or login with your details

Forgot password? Click here to reset