Regret Analysis of Posterior Sampling-Based Expected Improvement for Bayesian Optimization
Authors: Shion Takeno, Yu Inatsu, Masayuki Karasuyama, Ichiro Takeuchi
TMLR 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Finally, we demonstrate the effectiveness of the proposed method through numerical experiments. |
| Researcher Affiliation | Academia | Shion Takeno EMAIL Department of Mechanical Systems Engineering, Nagoya University RIKEN Center for Advanced Intelligence Project Yu Inatsu EMAIL Department of Computer Science, Nagoya Institute of Technology Masayuki Karasuyama EMAIL Department of Computer Science, Nagoya Institute of Technology Ichiro Takeuchi EMAIL Department of Mechanical Systems Engineering, Nagoya University RIKEN Center for Advanced Intelligence Project |
| Pseudocode | Yes | Algorithm 1 GP-EIMS Require: Input space X, GP prior µ = 0 and k, and initial dataset D0 1: for t = 1, . . . do 2: Fit GP to Dt 1 3: Generate a sample path gt p(f|Dt 1) 4: g t maxx X gt(x) 5: xt arg maxx X EI(µt 1(x), σt 1(x), g t ) 6: Observe yt = f(xt) + ϵt and Dt Dt 1 (xt, yt) 7: end for |
| Open Source Code | No | The paper does not explicitly state that source code for the described methodology is released or provide a link to a code repository. It only mentions using existing approximations like "random Fourier feature approximations". |
| Open Datasets | Yes | We performed numerical experiments using synthetic functions generated from GPs, which match the assumptions for our analysis. ... Figures 1 and 2 show the simple regret and cumulative regret for the SE kernels. ... We performed the experiments for the Matérn kernels ... and several benchmark functions from https://www.sfu.ca/~ssurjano/optimization.html. |
| Dataset Splits | No | The paper states, "We set X = {0.0, 0.1, . . . , 0.9}d and d = 4. Therefore, |X| = 104." and "We set an initial dataset to data that is closest to 2d data generated randomly as a Sobol sequence." It does not explicitly mention training/test/validation splits or reference standard splits with citations for reproducibility. |
| Hardware Specification | No | The paper does not provide specific details about the hardware used to run the experiments, such as GPU/CPU models or memory specifications. |
| Software Dependencies | No | The paper mentions "random Fourier feature approximations" as a technique used but does not specify any software libraries, frameworks, or their version numbers. For example, it does not mention Python, PyTorch, TensorFlow, or specific library versions. |
| Experiment Setup | Yes | We set X = {0.0, 0.1, . . . , 0.9}d and d = 4. ... We employed the SE kernel k SE(x, x ) = exp x x 2 2/(2ℓ2) . ... We report results changing ℓ {0.1, 0.2} and σ {0.01, 0.1, 1}. We fixed the hyperparameters of the GP model, that is ℓand σ, to the parameters used to generate the synthetic functions and observation noise. ... We set the hyperparameters of GP-UCB, IRGP-UCB, and GP-EI-µmax to the theoretically derived parameters for the BCR analyses. Therefore, we set βt = 2 log(|X|t2/ 2π +1) for GP-UCB and ζt = 2 log(|X|/2)+Zt with Zt Exp(λ = 1/2) for IRGP-UCB (Takeno et al., 2023). Furthermore, we set νt = 2 log(|X|t2/ 2π + 1) for GP-EI-µmax (see Theorem B.4). The number of MC samples in MES, JES, and E3I was set to 10. |