# Tight Regret Bounds for Noisy Optimization of a Brownian Motion

Wang Zexin
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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 simple regret and the smallest possible expected cumulative regret scale as \$\Omega(1 / \sqrt{T \log (T)}) \cap \mathcal{O}(...More

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