  We propose information-directed sampling -- a new approach to online
optimization problems in which a decision-maker must balance between
exploration and exploitation while learning from partial feedback. Each action
is sampled in a manner that minimizes the ratio between squared expected
single-period regret and a measure of information gain: the mutual information
between the optimal action and the next observation. We establish an expected
regret bound for information-directed sampling that applies across a very
general class of models and scales with the entropy of the optimal action
distribution. We illustrate through simple analytic examples how
information-directed sampling accounts for kinds of information that
alternative approaches do not adequately address and that this can lead to
dramatic performance gains. For the widely studied Bernoulli, Gaussian, and
linear bandit problems, we demonstrate state-of-the-art simulation performance.
