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Randomized Gaussian Process Upper Confidence Bound with Tighter Bayesian Regret Bounds
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| 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 benchmarks | simple regret | Helped |
| Use two-parameter exponential randomization instead of Gamma randomization (RGP-UCB) | RGP-UCB · Benchmark functions | simple regret | Helped |
| Generalize RGP-UCB regret analysis to wider class of randomized confidence distributions (no distribution change) | RGP-UCB · Theory (finite and continuous domains) | BCR convergence rate | No clear effect |
| Two-parameter exponential randomization removes the need to increase confidence parameter with iterations | IRGP-UCB · Synthetic functions (theoretical confidence parameter) | confidence parameter value over iterations | Helped |
| Two-parameter exponential randomization (finite domain BCR bound) | IRGP-UCB · Finite domain theory | BCR convergence rate in T: O(sqrt(T gamma_T)) vs O(sqrt(T gamma_T log T)) | Helped |
| Two-parameter exponential randomization on continuous domain | IRGP-UCB · Continuous domain theory | BCR convergence rate in T | No 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_t | IRGP-UCB · Holder table function | simple regret | Helped |
| Two-parameter exponential randomization vs baselines on real materials datasets | IRGP-UCB · Perovskite, P3HT/CNT, AgNP datasets | simple regret | Mixed |
| Gamma-distributed randomized confidence (RGP-UCB) vs deterministic GP-UCB on synthetic functions | RGP-UCB · Synthetic functions | simple regret | No clear effect |
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