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.