Batched Energy-Entropy acquisition for Bayesian Optimization

TL;DR

Batched Energy-Entropy acquisition for BO (BEEBO) enables tight control of the explore-exploit trade-off of the optimization process and generalizes to heteroskedastic black-box problems, showing competitive performance to existing methods.

Abstract

Bayesian optimization (BO) is an attractive machine learning framework for performing sample-efficient global optimization of black-box functions. The optimization process is guided by an acquisition function that selects points to acquire in each round of BO. In batched BO, when multiple points are acquired in parallel, commonly used acquisition functions are often high-dimensional and intractable, leading to the use of sampling-based alternatives. We propose a statistical physics inspired acquisition function for BO with Gaussian processes that can natively handle batches. Batched Energy-Entropy acquisition for BO (BEEBO) enables tight control of the explore-exploit trade-off of the optimization process and generalizes to heteroskedastic black-box problems. We demonstrate the applicability of BEEBO on a range of problems, showing competitive performance to existing methods.

Figures (24)

• Figure 1: $q$-UCB does not allow for controlling its explore-exploit trade-off with large batches. A GP surrogate (background) was initialized with 100 random points of the Ackley function. $q$-UCB was run with $\kappa=0.1$ and $\kappa=100$, BEEBO with $T'$= 0.05 and $T'$=50. Batch size $Q$=100.
• Figure 2: Mean distances of acquired points to the different optima of the Branin function. Under heteroskedastic noise, BEEBO is risk-averse and preferentially optimizes towards the low-noise optimum 1. Under homoskedastic noise, there is no preference. $q$-UCB does not adapt its behaviour to noise, remaining risk-neutral. The means and standard deviations over five replicates are shown.
• Figure : meanBEEBO optimization
• Figure A1: The Branin function with added heteroskedastic noise following \ref{['eq:heteroskedastic_noise']}. $\sigma^{2}_{max}=100$, $\lambda=0.05$.
• Figure A2: Experiments on the 14D robot arm pushing and 60D rover trajectory planning control problems. 10 replicates each. GIBBON (s) refers to the scaled larged-batch variant of GIBBON.