Combinatorial Pure Exploration with Full-bandit Feedback and Beyond: Solving Combinatorial Optimization under Uncertainty with Limited Observation
This review addresses the practical challenge of applying combinatorial optimization in real-world systems like recommender systems and communication networks, where input parameters are uncertain and feedback is limited, which is an incremental improvement over existing methods.
This paper reviews techniques for combinatorial pure exploration problems, specifically addressing scenarios with limited feedback where individual edge outcomes are not always accessible. It focuses on solving combinatorial optimization under uncertainty when input parameters like edge weights are initially unknown.
Combinatorial optimization is one of the fundamental research fields that has been extensively studied in theoretical computer science and operations research. When developing an algorithm for combinatorial optimization, it is commonly assumed that parameters such as edge weights are exactly known as inputs. However, this assumption may not be fulfilled since input parameters are often uncertain or initially unknown in many applications such as recommender systems, crowdsourcing, communication networks, and online advertisement. To resolve such uncertainty, the problem of combinatorial pure exploration of multi-armed bandits (CPE) and its variants have recieved increasing attention. Earlier work on CPE has studied the semi-bandit feedback or assumed that the outcome from each individual edge is always accessible at all rounds. However, due to practical constraints such as a budget ceiling or privacy concern, such strong feedback is not always available in recent applications. In this article, we review recently proposed techniques for combinatorial pure exploration problems with limited feedback.