Stochastic $k$-Submodular Bandits with Full Bandit Feedback

In this paper, we present the first sublinear 𝛼-regret bounds for online 𝑘-submodular optimization problems with full-bandit feedback, where 𝛼 is a corresponding offline approximation ratio. Specifically, we propose online algorithms for multiple 𝑘-submodular stochastic combinatorial multi-armed bandit problems, including (i) monotone functions and individual size constraints, (ii) monotone functions with matroid constraints, (iii) non-monotone functions with matroid constraints, (iv) non-monotone functions without constraints, and (v) monotone functions without constraints. We transform approximation algorithms for offline 𝑘-submodular maximization problems into online algorithms through the offline-toonline framework proposed by [9]. A key contribution of our work is analyzing the robustness of the offline algorithms.