Online Learning in the Random-Order Model

In the random-order model for online learning, the sequence of losses is chosen upfront by an adversary and presented to the learner after a random permutation. Any random-order input is asymptotically equivalent to a stochastic i.i.d.~one, but, for finite times, it may exhibit significant non-stationarity, which can hinder the performance of stochastic learning algorithms.While algorithms for adversarial inputs naturally maintain their regret guarantees in random order, simple no-regret algorithms exist for the stochastic model that fail against random-order instances. In this paper, we propose a general procedure to adapt stochastic learning algorithms to the random-order model without substantially affecting their regret guarantees. This allows us to recover improved regret bounds for prediction with delays, bandits with switching costs, and online learning with constraints. Finally, we investigate online classification and prove that, in random order, learnability is characterized by the VC dimension rather than by the Littlestone dimension, thus providing a further separation from the general adversarial model.

We study how to address online learning problems under random order inputs, which is an intermediate setting between the fully stochastic and fully adversarial input models.