Learning to Optimize via Information-Directed Sampling
This addresses the challenge of efficient decision-making in bandit problems for researchers and practitioners, offering a novel approach that can lead to dramatic performance gains.
The paper tackles the online optimization problem of balancing exploration and exploitation under partial feedback by proposing information-directed sampling, which minimizes the ratio of squared expected regret to information gain, and demonstrates state-of-the-art performance in simulations for Bernoulli, Gaussian, and linear bandit problems.
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.