Parallel Gaussian Process Optimization with Upper Confidence Bound and Pure Exploration

TL;DR

This paper introduces a parallel Gaussian Process optimization algorithm combining UCB and Pure Exploration, providing theoretical regret bounds and demonstrating empirical efficiency over existing methods.

Contribution

The paper presents GP-UCB-PE, a novel parallel optimization algorithm with proven regret bounds that improve over sequential methods and is validated empirically.

Findings

Regret bounds improve by sqrt{K} with batch size K.

Constants in bounds are dimension-free.

Empirical results outperform state-of-the-art methods.

Abstract

In this paper, we consider the challenge of maximizing an unknown function f for which evaluations are noisy and are acquired with high cost. An iterative procedure uses the previous measures to actively select the next estimation of f which is predicted to be the most useful. We focus on the case where the function can be evaluated in parallel with batches of fixed size and analyze the benefit compared to the purely sequential procedure in terms of cumulative regret. We introduce the Gaussian Process Upper Confidence Bound and Pure Exploration algorithm (GP-UCB-PE) which combines the UCB strategy and Pure Exploration in the same batch of evaluations along the parallel iterations. We prove theoretical upper bounds on the regret with batches of size K for this procedure which show the improvement of the order of sqrt{K} for fixed iteration cost over purely sequential versions. Moreover, the multiplicative constants involved have the property of being dimension-free. We also confirm empirically the efficiency of GP-UCB-PE on real and synthetic problems compared to state-of-the-art competitors.