Non-monotone Sequential Submodular Maximization

TL;DR

This paper addresses the challenge of maximizing a sum of non-monotone submodular functions through sequential selection and ranking of items, extending beyond the traditional monotone assumption to better model real-world scenarios like diversity-aware recommendations.

Contribution

It introduces the first algorithms for non-monotone sequential submodular maximization, covering flexible, fixed-length, and special cases, with empirical validation in video recommendation systems.

Findings

Proposed algorithms outperform baselines in experiments.

Effective in diverse applications like recommendation and assortment optimization.

Validated on real-world video recommendation data.

Abstract

In this paper, we study a fundamental problem in submodular optimization, which is called sequential submodular maximization. Specifically, we aim to select and rank a group of $k$ items from a ground set $V$ such that the weighted summation of $k$ (possibly non-monotone) submodular functions $f_1, \cdots ,f_k: 2^V \rightarrow \mathbb{R}^+$ is maximized, here each function $f_j$ takes the first $j$ items from this sequence as input. The existing research on sequential submodular maximization has predominantly concentrated on the monotone setting, assuming that the submodular functions are non-decreasing. However, in various real-world scenarios, like diversity-aware recommendation systems, adding items to an existing set might negatively impact the overall utility. In response, this paper pioneers the examination of the aforementioned problem with non-monotone submodular functions and offers effective solutions for both flexible and fixed length constraints, as well as a special case with identical utility functions. The empirical evaluations further validate the effectiveness of our proposed algorithms in the domain of video recommendations. The results of this research have implications in various fields, including recommendation systems and assortment optimization, where the ordering of items significantly impacts the overall value obtained.