Learning Submodular Sequencing from Samples

TL;DR

This paper introduces an algorithm for sequential submodular maximization using only sample data, applicable in real-world scenarios like product ranking, and extends existing optimization methods to sequence-dependent functions.

Contribution

It presents a novel algorithm that learns to sequence items from samples, extending prior work from set functions to sequence-dependent submodular functions.

Findings

Achieves approximation ratios based on submodular curvature.

Works with polynomially many samples from a two-stage distribution.

Effective in practical applications like online retail ranking.

Abstract

This paper addresses the problem of sequential submodular maximization: selecting and ranking items in a sequence to optimize some composite submodular function. In contrast to most of the previous works, which assume access to the utility function, we assume that we are given only a set of samples. Each sample includes a random sequence of items and its associated utility. We present an algorithm that, given polynomially many samples drawn from a two-stage uniform distribution, achieves an approximation ratio dependent on the curvature of individual submodular functions. Our results apply in a wide variety of real-world scenarios, such as ranking products in online retail platforms, where complete knowledge of the utility function is often impossible to obtain. Our algorithm gives an empirically useful solution in such contexts, thus proving that limited data can be of great use in sequencing tasks. From a technical perspective, our results extend prior work on ``optimization from samples'' by generalizing from optimizing a set function to a sequence-dependent function.