# Contextual Bandits with Random Projection

## TL;DR

This paper introduces CBRAP, a novel algorithm for high-dimensional linear contextual bandits that reduces computational complexity and regret bounds by employing random projections, making it suitable for large-scale data.

## Contribution

The paper presents CBRAP, a new high-dimensional linear bandit algorithm that leverages random projections to improve efficiency and relaxes previous sparsity assumptions.

## Key findings

- CBRAP achieves time efficiency in high-dimensional settings.
- The algorithm provides a linear upper regret bound.
- It relaxes the sparsity assumption in linear bandits.

## Abstract

Contextual bandits with linear payoffs, which are also known as linear bandits, provide a powerful alternative for solving practical problems of sequential decisions, e.g., online advertisements. In the era of big data, contextual data usually tend to be high-dimensional, which leads to new challenges for traditional linear bandits mostly designed for the setting of low-dimensional contextual data. Due to the curse of dimensionality, there are two challenges in most of the current bandit algorithms: the first is high time-complexity; and the second is extreme large upper regret bounds with high-dimensional data. In this paper, in order to attack the above two challenges effectively, we develop an algorithm of Contextual Bandits via RAndom Projection (\texttt{CBRAP}) in the setting of linear payoffs, which works especially for high-dimensional contextual data. The proposed \texttt{CBRAP} algorithm is time-efficient and flexible, because it enables players to choose an arm in a low-dimensional space, and relaxes the sparsity assumption of constant number of non-zero components in previous work. Besides, we provide a linear upper regret bound for the proposed algorithm, which is associated with reduced dimensions.