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Sub-linear Regret Bounds for Bayesian Optimisation in Unknown Search Spaces
Hung The Tran · Sunil Gupta · Santu Rana · Huong Ha · Svetha Venkatesh

Wed Dec 09 09:00 AM -- 11:00 AM (PST) @ Poster Session 3 #1061

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 \emph{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.

Author Information

Hung The Tran (Deakin University)
Sunil Gupta (Deakin University)
Santu Rana (Deakin University)
Huong Ha (RMIT University)
Svetha Venkatesh (Deakin University)

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