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

TL;DR

This paper reviews recent techniques for solving combinatorial optimization problems under uncertainty with limited feedback, addressing practical constraints like privacy and budget limits in applications such as recommender systems and networks.

Contribution

It provides a comprehensive review of recent methods for combinatorial pure exploration with limited feedback, extending beyond traditional semi-bandit feedback assumptions.

Findings

Summarizes recent algorithms for limited feedback scenarios.

Highlights challenges and solutions in practical applications.

Identifies open problems and future research directions.

Abstract

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.