It turns out that many different people use the term “Online Learning”, and often they don’t have the same definition in mind. Here’s a list of the possibilities I know of.

**Online Information Setting**Online learning refers to a*problem*in which unlabeled data comes, a prediction is made, and then feedback is acquired.**Online Adversarial Setting**Online learning refers to*algorithms*in the Online Information Setting which satisfy guarantees of the form: “For all possible sequences of observations, the algorithim has regret at most*log ( number of strategies)*with respect to the best strategy in a set.” This is sometimes called online learning with experts.**Online Optimization Constraint**Online learning refers to optimizing a predictor via a learning algorithm tunes parameters on a per-example basis. This may or may not be applied in the Online Information Setting, and the strategy may or may not satisfy Adversarial setting theory.**Online Computational Constraint**Online learning refers to an algorithmic constraint that the amount of computation per example is constant as the number of examples increases. Again, this doesn’t imply anything in particular about the Information setting in which it is applied.**Lifelong Learning**Online learning refers to learning in a setting where different tasks come at you over time, and you need to rapidly adapt to past mastered tasks.

Along the lines of 4., I would add:

Online Space ConstraintAn algorithmic constraint that the storage required by the learner does not grow with the number of seen examples.[…] The learning rate c plays a critical role in the theorem, and the best constant setting of c depends on how many total rounds T there are. Tong Zhang likes to think of this algorithm as the stochastic gradient descent with entropy regularization, which makes it clear that when used as an online optimization algorithm, c should be gradually decreased in value. […]

[…] and there is no necessary reason they must be.) And then there are non-traditional settings such as online learning, reinforcement learning, and active learning, where the structure of access to information in play. […]