Optimal Order Simple Regret for Gaussian Process Bandits
Authors: Sattar Vakili, Nacime Bouziani, Sepehr Jalali, Alberto Bernacchia, Da-shan Shiu
NeurIPS 2021 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We provide numerical experiments on the simple regret performance of MVR comparing it to GP-UCB [19, 20], GP-PI [26] and GP-EI [26]. |
| Researcher Affiliation | Collaboration | Media Tek Research {sattar.vakili, sepehr.jalali, alberto.bernacchia, ds.shiu}@mtkresearch.com +Imperial College London n.bouziani18@imperial.ac.uk |
| Pseudocode | Yes | Algorithm 1 Maximum Variance Reduction (MVR) 1: Initialization: k, X, f, σ2 0(x) k(x, x). 2: for n = 1, 2, . . . , N do 3: xn = argmaxx X σ2 n 1(x), where a tie is broken arbitrarily. 4: Update σ2 n(.) according to (2). 5: end for 6: Update µN(.) according to (2). 7: return ˆx N = argmaxx X µN(x), where a tie is broken arbitrarily. |
| Open Source Code | No | The paper does not provide an explicit statement or link for the open-sourcing of the code for its methodology. |
| Open Datasets | No | We follow the experiment set up in [20] to generate test functions from the RKHS. First, 100 points are uniformly sampled from interval [0, 1]. A GP sample with kernel k is drawn over these points. Given this sample, the mean of posterior distribution is used as the test function f. (The paper generates synthetic data, rather than using a publicly available dataset with concrete access information). |
| Dataset Splits | No | The paper describes generating synthetic data and testing, but does not provide specific train/validation/test dataset splits needed for reproducibility. |
| Hardware Specification | No | The paper does not provide any specific details about the hardware used to run the experiments. |
| Software Dependencies | No | The paper mentions algorithms like GP-UCB, GP-PI, GP-EI, but does not provide specific version numbers for any software or libraries used in the experiments. |
| Experiment Setup | Yes | Parameter λ2 is set to 1% of the function range. For IGP-UCB we set the parameters exactly as described in [20]. The GP model is equipped with SE or Matérn-2.5 kernel with l = 0.2. We use 2 different models for the noise: a zero mean Gaussian with variance equal to λ2 (a sub-Gaussian distribution) and a zero mean Laplace with scale parameter equal to λ (a light-tailed distribution). We run each experiment over 25 independent trials. |