  Partial monitoring is an expressive framework for sequential decision-making
with an abundance of applications, including graph-structured and dueling
bandits, dynamic pricing and transductive feedback models. We survey and extend
recent results on the linear formulation of partial monitoring that naturally
generalizes the standard linear bandit setting. The main result is that a
single algorithm, information-directed sampling (IDS), is (nearly) worst-case
rate optimal in all finite-action games. We present a simple and unified
analysis of stochastic partial monitoring, and further extend the model to the
contextual and kernelized setting.
