Online learning concerns the process of making sequential decisions in an adversarial environment. We first introduce algorithms in the traditional online learning setting. In the traditional setting, the learner’s objective is to select actions to minimize the loss or maximize the reward. In addition to this objective, there are other constraints that need to be satisfied in the sequential decision process. We further discuss [1][2][3] online learning with long-term constraints, which develop algorithms that achieve sub-linear bound on both the regret and violation of constraints. At last, we explore alternative literature filed in online learning with abstention where [4][5] provide the algorithm with improved regret bound with rejections options.
