Regret Analysis for Randomized Gaussian Process Upper Confidence Bound

Authors: Shion Takeno, Yu Inatsu, Masayuki Karasuyama

JAIR 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Experimental Finally, we show numerical experiments using synthetic and benchmark functions and real-world emulators.
Researcher Affiliation Academia SHION TAKENO , Nagoya University, Japan and RIKEN AIP, Japan YU INATSU, Nagoya Institute of Technology, Japan MASAYUKI KARASUYAMA, Nagoya Institute of Technology, Japan Authors Contact Information: Shion Takeno, orcid: 0009-0000-3638-8658, EMAIL, Nagoya University, Nagoya, Aichi, Japan and RIKEN AIP, Nihonbashi, Tokyo, Japan; Yu Inatsu, orcid: 0000-0001-5655-2558, EMAIL, Nagoya Institute of Technology, Nagoya, Aichi, Japan; Masayuki Karasuyama, orcid: 0000-0002-6177-3686, EMAIL, Nagoya Institute of Technology, Nagoya, Aichi, Japan.
Pseudocode Yes Algorithm 1 IRGP-UCB Require: Input space X, Parameters {𝑠𝑑}𝑑 1 and πœ†for πœπ‘‘, GP prior πœ‡= 0 and π‘˜ 1: D0 2: for 𝑑= 1, . . . do 3: Fit GP to D𝑑 1 4: Generate πœπ‘‘by Eq. (1) 5: 𝒙𝑑 arg max𝒙 X πœ‡π‘‘ 1(𝒙) + 𝜁1/2 𝑑 πœŽπ‘‘ 1(𝒙) 6: Observe 𝑦𝑑= 𝑓(𝒙𝑑) + πœ–π‘‘and D𝑑 D𝑑 1 (𝒙𝑑,𝑦𝑑)
Open Source Code No The paper does not contain any explicit statement about releasing source code for the described methodology, nor does it provide a link to a code repository.
Open Datasets Yes We employ three benchmark functions called Holder table (𝑑= 2), Cross in tray(𝑑= 2), and Ackley (𝑑= 4) functions, whose analytical forms are shown at https://www.sfu.ca/~ssurjano/optimization.html. This section provides the experimental results on the materials datasets provided in Liang et al. (2021). In the perovskite dataset (Sun et al. 2021), we optimize environmental stability with respect to composition parameters for halide perovskite (𝑑= 3 and |X| = 94). In the P3HT/CNT dataset (Bash et al. 2021), we optimize electrical conductivity with respect to composition parameters for the carbon nanotube polymer blend (𝑑= 5 and |X| = 178). In the Ag NP dataset (Mekki-Berrada et al. 2021), we optimize the absorbance spectrum of synthesized silver nanoparticles with respect to processing parameters for synthesizing triangular nanoprisms (𝑑= 5 and |X| = 164). See Liang et al. (2021) for more details about each dataset.
Dataset Splits No Ten synthetic functions and ten initial training datasets are randomly generated. Thus, the average and standard error for 10 10 trials are reported. For each function, we report the average and standard error for 10 trials using ten random initial datasets D0, where |D0| = 2𝑑. We set the initial dataset size |D0| = 2 as with Liang et al. (2021). The paper mentions initial dataset sizes and random generation but does not specify training/validation/test splits, or cross-validation details for the overall experimental process beyond these initial samples.
Hardware Specification No The paper describes numerical experiments and real-world dataset evaluations but does not provide specific details about the hardware (e.g., GPU models, CPU types, memory) used to run these experiments.
Software Dependencies No The paper mentions using a 'Gaussian kernel' and 'marginal likelihood maximization (Rasmussen and Williams 2005)' but does not specify particular software libraries or their version numbers, such as Python libraries (e.g., PyTorch, TensorFlow, scikit-learn) or other solvers with explicit version numbers.
Experiment Setup Yes We set the noise variance 𝜎2 = 10 4. The hyperparameters for GP are fixed to those used to generate the synthetic functions. The confidence parameters for GP-UCB, RGP-UCB, and IRGP-UCB are set as in Figure 1. We used the Gaussian kernel with automatic relevance determination, whose hyperparameter was selected by marginal likelihood maximization (Rasmussen and Williams 2005) per 5 iterations. For GP-UCB, we set the confidence parameter as 𝛽𝑑= 0.2𝑑log(2𝑑), which is the heuristic used in Kandasamy et al. (2017, 2015). For RGP-UCB, we set πœπ‘‘ Gamma(πœ…π‘‘,πœƒ= 1) with πœ…π‘‘= 0.2𝑑log(2𝑑) since E[πœπ‘‘] must have the same order as 𝛽𝑑(note that E[πœπ‘‘] = πœƒπœ…π‘‘). For IRGP-UCB, we set 𝑠= 𝑑/2 and πœ†= 1/2. We set the initial dataset size |D0| = 2 as with Liang et al. (2021). ... we optimized the hyperparameters of the RBF kernel in each iteration to avoid repeatedly obtaining samples using an inappropriate hyperparameter. The other settings matched those used in the benchmark function experiments.