Incentivizing Combinatorial Bandit Exploration
This addresses the problem of incentivized exploration for large, structured action sets in recommendation systems, representing a novel extension beyond prior work on small, unstructured sets.
The paper tackles incentivizing users to follow exploration recommendations in combinatorial semi-bandits, proving that Thompson Sampling is incentive-compatible with sufficient initial samples and designing algorithms to collect these samples.
Consider a bandit algorithm that recommends actions to self-interested users in a recommendation system. The users are free to choose other actions and need to be incentivized to follow the algorithm's recommendations. While the users prefer to exploit, the algorithm can incentivize them to explore by leveraging the information collected from the previous users. All published work on this problem, known as incentivized exploration, focuses on small, unstructured action sets and mainly targets the case when the users' beliefs are independent across actions. However, realistic exploration problems often feature large, structured action sets and highly correlated beliefs. We focus on a paradigmatic exploration problem with structure: combinatorial semi-bandits. We prove that Thompson Sampling, when applied to combinatorial semi-bandits, is incentive-compatible when initialized with a sufficient number of samples of each arm (where this number is determined in advance by the Bayesian prior). Moreover, we design incentive-compatible algorithms for collecting the initial samples.