Linear Submodular Maximization with Bandit Feedback

Submodular optimization with bandit feedback has recently been studied in a variety of contexts. In a number of real-world applications such as diversified recommender systems and data summarization, the submodular function exhibits additional linear structure. We consider developing approximation algorithms for the maximization of a submodular objective function f:2U≥ 0, where f=∑ᵢ₌₁ᵈwᵢFᵢ. It is assumed that we have value oracle access to the functions Fᵢ, but the coefficients wᵢ are unknown, and f can only be accessed via noisy queries. We develop algorithms for this setting inspired by adaptive allocation algorithms in the best-arm identification for linear bandit, with approximation guarantees arbitrarily close to the setting where we have value oracle access to f. Finally, we empirically demonstrate that our algorithms make vast improvements in terms of sample efficiency compared to algorithms that do not exploit the linear structure of f on instances of move recommendation.