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Combinatorial optimization is one of the fundamental research fields that hasbeen extensively studied in theoretical computer science and operationsresearch. When developing an algorithm for combinatorial optimization, it iscommonly assumed that parameters such as edge weights are exactly known asinputs. However, this assumption may not be fulfilled since input parametersare often uncertain or initially unknown in many applications such asrecommender systems, crowdsourcing, communication networks, and onlineadvertisement. To resolve such uncertainty, the problem of combinatorial pureexploration of multi-armed bandits (CPE) and its variants have recievedincreasing attention. Earlier work on CPE has studied the semi-bandit feedbackor assumed that the outcome from each individual edge is always accessible atall rounds. However, due to practical constraints such as a budget ceiling orprivacy concern, such strong feedback is not always available in recentapplications. In this article, we review recently proposed techniques forcombinatorial pure exploration problems with limited feedback.

Combinatorial Pure Exploration with Full-bandit Feedback and Beyond: Solving Combinatorial Optimization under Uncertainty with Limited Observation