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Bayesian optimisation is a popular, surrogate model-based approach foroptimising expensive black-box functions. Given a surrogate model, the nextlocation to expensively evaluate is chosen via maximisation of a cheap-to-queryacquisition function. We present an $\epsilon$-greedy procedure for Bayesianoptimisation in batch settings in which the black-box function can be evaluatedmultiple times in parallel. Our $\epsilon$-shotgun algorithm leverages themodel's prediction, uncertainty, and the approximated rate of change of thelandscape to determine the spread of batch solutions to be distributed around aputative location. The initial target location is selected either in anexploitative fashion on the mean prediction, or -- with probability $\epsilon$-- from elsewhere in the design space. This results in locations that are moredensely sampled in regions where the function is changing rapidly and inlocations predicted to be good (i.e close to predicted optima), with morescattered samples in regions where the function is flatter and/or of poorerquality. We empirically evaluate the $\epsilon$-shotgun methods on a range ofsynthetic functions and two real-world problems, finding that they perform atleast as well as state-of-the-art batch methods and in many cases exceed theirperformance.

$\epsilon$-shotgun: $\epsilon$-greedy Batch Bayesian Optimisation