Instructions: 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: <lb>We consider online learning when the time horizon is unknown. We apply a<lb>minimax analysis, beginning with the fixed horizon case, and then moving on to<lb>two unknown-horizon settings, one that assumes the horizon is chosen randomly<lb>according to some known distribution, and the other which allows the adversary<lb>full control over the horizon. For the random horizon setting with restricted losses,<lb>we derive a fully optimal minimax algorithm. And for the adversarial horizon set-<lb>ting, we prove a nontrivial lower bound which shows that the adversary obtains<lb>strictly more power than when the horizon is fixed and known. Based on the mini-<lb>max solution of the random horizon setting, we then propose a new adaptive algo-<lb>rithm which "pretends" that the horizon is drawn from a distribution from a special<lb>family, but no matter how the actual horizon is chosen, the worst-case regret is of<lb>the optimal rate. Furthermore, our algorithm can be generalized in many ways,<lb>including handling other unknown information and other online learning settings.<lb>Experiments show that our algorithm outperforms many other existing algorithms<lb>in an online linear optimization setting.
Output:
Online Learning with Unknown Time Horizon