Optimistic Optimization of Gaussian Process Samples

TL;DR

This paper explores combining the efficiency of optimistic optimization with the modeling power of Bayesian optimization by mapping kernels to dissimilarities, enabling faster global optimization for certain problems.

Contribution

It introduces a novel optimistic optimization algorithm for Bayesian settings by mapping kernels to dissimilarities, achieving up to O(N log N) runtime.

Findings

Optimistic optimization can outperform Bayesian optimization for low-cost evaluations with stationary kernels.

Bayesian optimization performs better for complex, parametric models.

The work identifies a new research area bridging geometric and probabilistic search methods.

Abstract

Bayesian optimization is a popular formalism for global optimization, but its computational costs limit it to expensive-to-evaluate functions. A competing, computationally more efficient, global optimization framework is optimistic optimization, which exploits prior knowledge about the geometry of the search space in form of a dissimilarity function. We investigate to which degree the conceptual advantages of Bayesian Optimization can be combined with the computational efficiency of optimistic optimization. By mapping the kernel to a dissimilarity, we obtain an optimistic optimization algorithm for the Bayesian Optimization setting with a run-time of up to $\mathcal{O}(N \log N)$. As a high-level take-away we find that, when using stationary kernels on objectives of relatively low evaluation cost, optimistic optimization can be strongly preferable over Bayesian optimization, while for strongly coupled and parametric models, good implementations of Bayesian optimization can perform much better, even at low evaluation cost. We argue that there is a new research domain between geometric and probabilistic search, i.e. methods that run drastically faster than traditional Bayesian optimization, while retaining some of the crucial functionality of Bayesian optimization.