Learning to Optimize via Information-Directed Sampling

We propose information-directed sampling -- a new algorithm for 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. For the widely studied Bernoulli, Gaussian, and linear bandit problems, we demonstrate simulation performance surpassing popular approaches, including upper confidence bound algorithms, Thompson sampling, and the knowledge gradient algorithm. Further, we present simple analytic examples illustrating that, due to the way it measures information gain, information-directed sampling can dramatically outperform upper confidence bound algorithms and Thompson sampling.