Adversarial Online Learning with Changing Action Sets: Efficient Algorithms with Approx Regret Bo...

The 32nd International Conference on Algorithmic Learning Theory (ALT 2021)

Title: Adversarial Online Learning with Changing Action Sets: Efficient Algorithms with Approximate Regret Bounds
Authors: Ehsan Emamjomeh-Zadeh, Chen-Yu Wei, Haipeng Luo, David Kempe
Speaker: Chen-Yu Wei

Abstract:

We revisit the problem of online learning with sleeping experts/bandits: in each time step, only a subset of the actions are available for the algorithm to choose from (and learn about). The work of Kleinberg et al. (2010) showed that there exist no-regret algorithms which perform no worse than the best ranking of actions asymptotically. Unfortunately, achieving this regret bound appears computationally hard: Kanade and Steinke (2014) showed that achieving this no-regret performance is at least as hard as PAC-learning DNFs, a notoriously difficult problem.
In the present work, we relax the original problem and study computationally efficient no-approximate-regret algorithms: such algorithms may exceed the optimal cost by a multiplicative constant in addition to the additive regret. We give an algorithm that provides a no-approximate-regret guarantee for the general sleeping expert/bandit problems. For several canonical special cases of the problem, we give algorithms with significantly better approximation ratios; these algorithms also illustrate different techniques for achieving no-approximate-regret guarantees.