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We investigate the problem of unconstrained combinatorial multi-armed banditswith full-bandit feedback and stochastic rewards for submodular maximization.Previous works investigate the same problem assuming a submodular and monotonereward function. In this work, we study a more general problem, i.e., when thereward function is not necessarily monotone, and the submodularity is assumedonly in expectation. We propose Randomized Greedy Learning (RGL) algorithm andtheoretically prove that it achieves a $\frac{1}{2}$-regret upper bound of$\tilde{\mathcal{O}}(n T^{\frac{2}{3}})$ for horizon $T$ and number of arms$n$. We also show in experiments that RGL empirically outperforms otherfull-bandit variants in submodular and non-submodular settings.

Randomized Greedy Learning for Non-monotone Stochastic Submodular Maximization Under Full-bandit Feedback