Definition: In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.
Input: We improve the regret bound of the Upper Confidence Bound (UCB) algorithm of Auer et al. (2002) and show that its regret is with high-probability a problem dependent constant. In the case of linear bandits (Dani et al., 2008), we improve the problem dependent bound in the dimension and number of time steps. Furthermore, as opposed to the previous result, we prove that our bound holds for small sample sizes, and at the same time the worst case bound is improved by a logarithmic factor and the constant is improved.

Online Least Squares Estimation with Self-Normalized Processes: An Application to Bandit Problems∗