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- W3002762179 abstract "We consider the problem of Bayesian optimization of a one-dimensional Brownian motion in which the $T$ adaptively chosen observations are corrupted by Gaussian noise. We show that as the smallest possible expected cumulative regret and the smallest possible expected simple regret scale as $Omega(sigmasqrt{T / log (T)}) cap mathcal{O}(sigmasqrt{T} cdot log T)$ and $Omega(sigma / sqrt{T log (T)}) cap mathcal{O}(sigmalog T / sqrt{T})$ respectively, where $sigma^2$ is the noise variance. Thus, our upper and lower bounds are tight up to a factor of $mathcal{O}( (log T)^{1.5} )$. The upper bound uses an algorithm based on confidence bounds and the Markov property of Brownian motion (among other useful properties), and the lower bound is based on a reduction to binary hypothesis testing." @default.
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- W3002762179 date "2022-01-01" @default.
- W3002762179 modified "2023-10-17" @default.
- W3002762179 title "Tight Regret Bounds for Noisy Optimization of a Brownian Motion" @default.
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- W3002762179 doi "https://doi.org/10.1109/tsp.2022.3144939" @default.
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