BOO achieves exponentially decaying regret O(N^{-√N}) by combining Bayesian optimisation and partitioning-based optimistic optimisation for Matérn GP functions with ν > 4 + D/2.
Given a set of pointsDp−1 , we define the fill distanceFD(Dp−1,X ) as the largest distance from any point inX to the points inDp−1, as FD(Dp−1,X ) = supx∈X infci∈Dp−1||x−ci||
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Bayesian Optimistic Optimisation with Exponentially Decaying Regret
BOO achieves exponentially decaying regret O(N^{-√N}) by combining Bayesian optimisation and partitioning-based optimistic optimisation for Matérn GP functions with ν > 4 + D/2.