CORe: Capitalizing On Rewards in Bandit Exploration
This work addresses the challenge of data-dependent exploration in bandit algorithms for machine learning, offering a parameter-free method that is incremental in improving exploration efficiency.
The paper tackles the problem of bandit exploration by proposing CORe, an algorithm that explores by randomizing past observations and exploits reward variance for optimism, achieving a gap-free regret bound of $ ilde O(d\sqrt{n\log K})$ in stochastic linear bandits.
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.