We consider the stochastic contextual bandit problem under the high dimensional linear model. We focus on the case where the action space is finite and random, with each action associated with a randomly generated contextual covariate. This setting finds essential applications such as personalized recommendation, online advertisement, and personalized medicine. However, it is very challenging as we need to balance exploration and exploitation. We propose doubly growing epochs and estimating the parameter using the best subset selection method, which is easy to implement in practice. This approach achieves Orps?Tq regret with high probability, which is nearly independent in the “ambient” regression model dimension d. We further attain a sharper Orp?sTq regret by using the SUPLINUCB framework and match the minimax lower bound of low-dimensional linear stochastic bandit problems. Finally, we conduct extensive numerical experiments to demonstrate the applicability and robustness of our algorithms empirically.
|Original language||English (US)|
|State||Published - Sep 4 2020|
- Best subset selection
- High-dimensional models
- Regret analysis
- Stochastic bandit
ASJC Scopus subject areas