  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.
