Bayesian Multi-Scale Optimistic Optimization
نویسندگان
چکیده
where σ T (x) = κ(x,x) − k1:T (x)K−1k1:T (x) and this bound is tight. Moreover, σ T (x) is the posterior predictive variance of a Gaussian process with the same kernel. Lemma 3 (Adapted from Proposition 1 of de Freitas et al. (2012)). Let κ : R × R → R be a kernel that is twice differentiable along the diagonal {(x,x) |x ∈ RD}, with L defined as in Lemma 1.1, and f be an element of the RKHS with kernel κ. If f is evaluated at point x, then for any other point y we have σT (y) ≤ L�x− y�.
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