Adversarial Online Learning with Changing Action Sets: Efficient Algorithms with Approximate Regret Bounds
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.
Cite
@article{arxiv.2003.03490,
title = {Adversarial Online Learning with Changing Action Sets: Efficient Algorithms with Approximate Regret Bounds},
author = {Ehsan Emamjomeh-Zadeh and Chen-Yu Wei and Haipeng Luo and David Kempe},
journal= {arXiv preprint arXiv:2003.03490},
year = {2021}
}