We establish a connection between the stability of mirror descent and the information ratio by Russo and Van Roy [2014]. Our analysis shows that mirror descent with suitable loss estimators and exploratory distributions enjoys the same bound on the adversarial regret as the bounds on the Bayesian regret for information-directed sampling. Along the way, we develop the theory for information-directed sampling and provide an efficient algorithm for adversarial bandits for which the regret upper bound matches exactly the best known information-theoretic upper bound.
@article{arxiv.2009.12228,
title = {Mirror Descent and the Information Ratio},
author = {Tor Lattimore and András György},
journal= {arXiv preprint arXiv:2009.12228},
year = {2020}
}