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arXiv · 2009.02539

Sub-linear Regret Bounds for Bayesian Optimisation in Unknown Search Spaces

Hung Tran-The·Sunil Gupta·Santu Rana·Huong Ha·Svetha Venkatesh
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Abstract

Bayesian optimisation is a popular method for efficient optimisation of expensive black-box functions. Traditionally, BO assumes that the search space is known. However, in many problems, this assumption does not hold. To this end, we propose a novel BO algorithm which expands (and shifts) the search space over iterations based on controlling the expansion rate thought a hyperharmonic series. Further, we propose another variant of our algorithm that scales to high dimensions. We show theoretically that for both our algorithms, the cumulative regret grows at sub-linear rates. Our experiments with synthetic and real-world optimisation tasks demonstrate the superiority of our algorithms over the current state-of-the-art methods for Bayesian optimisation in unknown search space.

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BibTeXRIS

Hung Tran-The, Sunil Gupta, Santu Rana, Huong Ha, Svetha Venkatesh. 2020-09-05. Sub-linear Regret Bounds for Bayesian Optimisation in Unknown Search Spaces. https://doi.org/10.5555/3495724.3497089

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