Several real-world problems in engineering and applied science require the selection of sequences that maximize a given reward function. Optimizing over sequences as opposed to sets requires exploring an exponentially larger search space and can become prohibitive in most cases of practical interest. However, if the objective function is submodular (intuitively, it exhibits a diminishing return property), the optimization problem becomes more manageable. Recently, there has been increasing interest in sequence submodularity in connection with applications such as recommender systems and online ad allocation. However, mostly ad hoc models and solutions have emerged within these applicative contexts. In consequence, the field appears fragmented and lacks coherence. In this paper, we offer a unified view of sequence submodularity and provide a generalized greedy algorithm that enjoys strong theoretical guarantees. We show how our approach naturally captures several application domains, and our algorithm encompasses existing methods, improving over them.

工程和应用科学中的一些实际问题需要选择使给定奖励函数最大化的序列。针对序列而不是集合进行优化需要探索指数级更大的搜索空间，并且在大多数实际感兴趣的情况下可能会变得无所适从。但是，如果目标函数是次模的（直观上讲，它的返回特性递减），则优化问题将变得更易于管理。最近，人们对序列亚模块性的兴趣日益浓厚与推荐系统和在线广告分配之类的应用结合使用。但是，在这些应用环境中，出现了大多数临时模型和解决方案。结果，该领域显得支离破碎并且缺乏连贯性。在本文中，我们提供了序列子模量的统一视图，并提供了具有强大理论保证的广义贪婪算法。我们展示了我们的方法如何自然地捕获多个应用程序域，并且我们的算法涵盖了现有方法，并对它们进行了改进。