CORe: Capitalizing On Rewards in Bandit Exploration

TL;DR

CORe is a data-dependent bandit algorithm that explores by randomizing past observations, achieving adaptive exploration without external noise, and demonstrating strong theoretical and empirical performance.

Contribution

The paper introduces CORe, a novel bandit algorithm that exploits reward variance for exploration, providing a general, parameter-free, and adaptive approach with theoretical guarantees.

Findings

Achieves $ ilde O(d ext{sqrt}(n ext{log} K))$ regret bound in linear bandits

Demonstrates superior empirical performance on synthetic and real-world data

Explores purely through past reward variance without external noise

Abstract

We propose a bandit algorithm that explores purely by randomizing its past observations. In particular, the sufficient optimism in the mean reward estimates is achieved by exploiting the variance in the past observed rewards. We name the algorithm Capitalizing On Rewards (CORe). The algorithm is general and can be easily applied to different bandit settings. The main benefit of CORe is that its exploration is fully data-dependent. It does not rely on any external noise and adapts to different problems without parameter tuning. We derive a $\tilde O(d\sqrt{n\log K})$ gap-free bound on the $n$-round regret of CORe in a stochastic linear bandit, where $d$ is the number of features and $K$ is the number of arms. Extensive empirical evaluation on multiple synthetic and real-world problems demonstrates the effectiveness of CORe.