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Randomized Gaussian Process Upper Confidence Bound with Tighter Bayesian Regret Bounds

ICML 2023 · Bandits and online learning › Contextual bandits and Thompson sampling · approach: Gaussian process bandit regret · 2 citations (OpenAlex)

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Measured effects reported in the paper

What was changedWhereMeasuredEffect
Replace GP-UCB's log-growing beta_t with randomized zeta_t from two-parameter exponential distribution (IRGP-UCB)GP-UCB · Holder table, Cross in tray, Ackley benchmarkssimple regretHelped
Use two-parameter exponential randomization instead of Gamma randomization (RGP-UCB)RGP-UCB · Benchmark functionssimple regretHelped
Generalize RGP-UCB regret analysis to wider class of randomized confidence distributions (no distribution change)RGP-UCB · Theory (finite and continuous domains)BCR convergence rateNo clear effect
Two-parameter exponential randomization removes the need to increase confidence parameter with iterationsIRGP-UCB · Synthetic functions (theoretical confidence parameter)confidence parameter value over iterationsHelped
Two-parameter exponential randomization (finite domain BCR bound)IRGP-UCB · Finite domain theoryBCR convergence rate in T: O(sqrt(T gamma_T)) vs O(sqrt(T gamma_T log T))Helped
Two-parameter exponential randomization on continuous domainIRGP-UCB · Continuous domain theoryBCR convergence rate in TNo clear effect
Set zeta via two-parameter exponential with s=d/2, lambda=1/2 in heuristic setting, versus Gamma-based RGP-UCB and GP-UCB heuristic beta_tIRGP-UCB · Holder table functionsimple regretHelped
Two-parameter exponential randomization vs baselines on real materials datasetsIRGP-UCB · Perovskite, P3HT/CNT, AgNP datasetssimple regretMixed
Gamma-distributed randomized confidence (RGP-UCB) vs deterministic GP-UCB on synthetic functionsRGP-UCB · Synthetic functionssimple regretNo clear effect

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