Trusted-Maximizers Entropy Search for Efficient Bayesian Optimization

TL;DR

This paper introduces Trusted-Maximizers Entropy Search (TES), a novel Bayesian optimization acquisition function that efficiently measures information gain about the maximizer, improving scalability and performance in batch settings.

Contribution

The paper proposes TES, a new information-based acquisition function for Bayesian optimization that reduces computational complexity and enhances batch optimization capabilities.

Findings

TES performs well on synthetic benchmarks.

TES effectively optimizes hyperparameters of neural networks.

TES scales to larger batch sizes in experiments.

Abstract

Information-based Bayesian optimization (BO) algorithms have achieved state-of-the-art performance in optimizing a black-box objective function. However, they usually require several approximations or simplifying assumptions (without clearly understanding their effects on the BO performance) and/or their generalization to batch BO is computationally unwieldy, especially with an increasing batch size. To alleviate these issues, this paper presents a novel trusted-maximizers entropy search (TES) acquisition function: It measures how much an input query contributes to the information gain on the maximizer over a finite set of trusted maximizers, i.e., inputs optimizing functions that are sampled from the Gaussian process posterior belief of the objective function. Evaluating TES requires either only a stochastic approximation with sampling or a deterministic approximation with expectation propagation, both of which are investigated and empirically evaluated using synthetic benchmark objective functions and real-world optimization problems, e.g., hyperparameter tuning of a convolutional neural network and synthesizing 'physically realizable' faces to fool a black-box face recognition system. Though TES can naturally be generalized to a batch variant with either approximation, the latter is amenable to be scaled to a much larger batch size in our experiments.