We study monotone submodular maximization under general matroid constraints in the online setting. We prove that online optimization of a large class of submodular functions, namely, weighted threshold potential functions, reduces to online convex optimization (OCO). This is precisely because functions in this class admit a concave relaxation; as a result, OCO policies, coupled with an appropriate rounding scheme, can be used to achieve sublinear regret in the combinatorial setting. We show that our reduction extends to many different versions of the online learning problem, including the dynamic regret, bandit, and optimistic-learning settings.

翻译：我们研究在线环境下一般拟阵约束下的单调子模最大化问题。我们证明，一大类子模函数（即加权阈值势函数）的在线优化可简化为在线凸优化（OCO）。这是因为该类函数具有凹松弛性质；因此，结合适当的取整方案，OCO策略可在组合设置中实现次线性遗憾。我们证明，该简化方法可推广至在线学习问题的多种不同变体，包括动态遗憾、Bandit和乐观学习等场景。