Unified Projection-Free Algorithms for Adversarial DR-Submodular
  Optimization
Mohammad Pedramfar Yididiya Y. Nadew Christopher J. Quinn Vaneet Aggarwal
This paper introduces unified projection-free Frank-Wolfe type algorithms for
adversarial continuous DR-submodular optimization, spanning scenarios such as
full information and (semi-)bandit feedback, monotone and non-monotone
functions, different constraints, and types of stochastic queries. For every
problem considered in the non-monotone setting, the proposed algorithms are
either the first with proven sub-linear $\alpha$-regret bounds or have better
$\alpha$-regret bounds than the state of the art, where $\alpha$ is a
corresponding approximation bound in the offline setting. In the monotone
setting, the proposed approach gives state-of-the-art sub-linear
$\alpha$-regret bounds among projection-free algorithms in 7 of the 8
considered cases while matching the result of the remaining case. Additionally,
this paper addresses semi-bandit and bandit feedback for adversarial
DR-submodular optimization, advancing the understanding of this optimization
area.