9 papers
On Regret Bounds of Thompson Sampling for Bayesian Optimization
Shion Takeno, Shogo Iwazaki
We study a widely used Bayesian optimization method, Gaussian process Thompson sampling (GP-TS), under the assumption that the objective function is a sample path from a GP. Compar…
Nearly-Optimal Algorithm for Adversarial Kernelized Bandits
Shogo Iwazaki
This paper studies kernelized bandits (also known as Gaussian process bandits) in an adversarial environment, where the reward functions in a known reproducing kernel Hilbert space…
Tighter Regret Lower Bound for Gaussian Process Bandits with Squared Exponential Kernel in Hypersphere
Shogo Iwazaki
We study an algorithm-independent, worst-case lower bound for the Gaussian process (GP) bandit problem in the frequentist setting, where the reward function is fixed and has a boun…
Improved Regret Bounds for Gaussian Process Upper Confidence Bound in Bayesian Optimization
Shogo Iwazaki
This paper addresses the Bayesian optimization problem (also referred to as the Bayesian setting of the Gaussian process bandit), where the learner seeks to minimize the regret und…
Gaussian Process Upper Confidence Bound Achieves Nearly-Optimal Regret in Noise-Free Gaussian Process Bandits
Shogo Iwazaki
We study the noise-free Gaussian Process (GP) bandits problem, in which the learner seeks to minimize regret through noise-free observations of the black-box objective function lyi…
High-dimensional Nonparametric Contextual Bandit Problem
Shogo Iwazaki, Junpei Komiyama, Masaaki Imaizumi
We consider the kernelized contextual bandit problem with a large feature space. This problem involves arms, and the goal of the forecaster is to maximize the cumulative reward…