High-dimensional Nonparametric Contextual Bandit Problem

Abstract

We consider the kernelized contextual bandit problem with a large feature space. This problem involves K arms, and the goal of the forecaster is to maximize the cumulative rewards through learning the relationship between the contexts and the rewards. It serves as a general framework for various decision-making scenarios, such as personalized online advertising and recommendation systems. Kernelized contextual bandits generalize the linear contextual bandit problem and offers a greater modeling flexibility. Existing methods, when applied to Gaussian kernels, yield a trivial bound of O(T) when we consider ( T) feature dimensions. To address this, we introduce stochastic assumptions on the context distribution and show that no-regret learning is achievable even when the number of dimensions grows up to the number of samples. Furthermore, we analyze lenient regret, which allows a per-round regret of at most > 0. We derive the rate of lenient regret in terms of .

Tasks

Reproductions