Scaling Gaussian Process Optimization by Evaluating a Few Unique Candidates Multiple Times

TL;DR

This paper introduces a method to improve Gaussian process optimization efficiency by limiting candidate switches, reducing computational costs while maintaining theoretical guarantees, especially useful in high-cost evaluation scenarios.

Contribution

It proposes a novel approach to restrict candidate switching in GP-Opt, enabling exact and efficient posterior computation, with modifications to GP-UCB and GP-EI algorithms.

Findings

Reduces runtime and memory complexity in GP-Opt.

Maintains no-regret guarantees with fewer candidate switches.

Enhances batching and parallel evaluation capabilities.

Abstract

Computing a Gaussian process (GP) posterior has a computational cost cubical in the number of historical points. A reformulation of the same GP posterior highlights that this complexity mainly depends on how many \emph{unique} historical points are considered. This can have important implication in active learning settings, where the set of historical points is constructed sequentially by the learner. We show that sequential black-box optimization based on GPs (GP-Opt) can be made efficient by sticking to a candidate solution for multiple evaluation steps and switch only when necessary. Limiting the number of switches also limits the number of unique points in the history of the GP. Thus, the efficient GP reformulation can be used to exactly and cheaply compute the posteriors required to run the GP-Opt algorithms. This approach is especially useful in real-world applications of GP-Opt with high switch costs (e.g. switching chemicals in wet labs, data/model loading in hyperparameter optimization). As examples of this meta-approach, we modify two well-established GP-Opt algorithms, GP-UCB and GP-EI, to switch candidates as infrequently as possible adapting rules from batched GP-Opt. These versions preserve all the theoretical no-regret guarantees while improving practical aspects of the algorithms such as runtime, memory complexity, and the ability of batching candidates and evaluating them in parallel.