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Tight Regret Bounds for Bayesian Optimization in One Dimension
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Algorithm with epoch-wise repeated sampling and shrinking sets of potential maximizers (vs. GP-UCB style strategies implied by Srinivas et al. bounds) | Noisy Bayesian optimization in one dimension (Matérn-ν kernel, ν>2) · Cumulative regret upper bound, 1D BO | Cumulative regret exponent in T: O*(T^0.5) vs O*(T^0.625) for ν=3 | Helped |
| Noise variance lower-bounded by cσ/T^(1-ζ) (mild condition) in analysis of the algorithm | Upper bound analysis · Theory, 1D BO | Regret bound | No clear effect |
| Resampling each point K(i) times consecutively within epochs | Proposed algorithm for noisy BO in 1D · Theory, 1D BO | Cumulative regret bound | Helped |
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