Randomized Greedy Learning for Non-monotone Stochastic Submodular Maximization Under Full-bandit Feedback
This addresses a more general bandit optimization problem for machine learning applications, though it is incremental by extending prior monotone assumptions to non-monotone cases.
The paper tackles the problem of non-monotone stochastic submodular maximization under full-bandit feedback, proposing the Randomized Greedy Learning algorithm which achieves a 1/2-regret bound of O~(n T^{2/3}) and empirically outperforms other methods.
We investigate the problem of unconstrained combinatorial multi-armed bandits with full-bandit feedback and stochastic rewards for submodular maximization. Previous works investigate the same problem assuming a submodular and monotone reward function. In this work, we study a more general problem, i.e., when the reward function is not necessarily monotone, and the submodularity is assumed only in expectation. We propose Randomized Greedy Learning (RGL) algorithm and theoretically 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 other full-bandit variants in submodular and non-submodular settings.