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 {π π‘}π‘ 1 and πfor ππ‘, GP prior π= 0 and π 1: D0 2: for π‘= 1, . . . do 3: Fit GP to Dπ‘ 1 4: Generate ππ‘by Eq. (1) 5: ππ‘ arg maxπ X ππ‘ 1(π) + π1/2 π‘ ππ‘ 1(π) 6: Observe π¦π‘= π(ππ‘) + ππ‘and Dπ‘ Dπ‘ 1 (ππ‘,π¦π‘) |
| 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 (π= 2), Cross in tray(π= 2), and Ackley (π= 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 (π= 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 (π= 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 (π= 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| = 2π. 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 π2 = 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 π½π‘= 0.2πlog(2π‘), which is the heuristic used in Kandasamy et al. (2017, 2015). For RGP-UCB, we set ππ‘ Gamma(π π‘,π= 1) with π π‘= 0.2πlog(2π‘) since E[ππ‘] must have the same order as π½π‘(note that E[ππ‘] = ππ π‘). For IRGP-UCB, we set π = π/2 and π= 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. |