Do Less, Get More: Streaming Submodular Maximization with Subsampling

TL;DR

This paper introduces a novel one-pass streaming algorithm for submodular maximization that uses subsampling to achieve tight approximation guarantees, minimal memory, and low function evaluations, enabling scalable machine learning applications.

Contribution

It presents the first streaming algorithm that combines subsampling with streaming for submodular maximization, offering improved efficiency and scalability.

Findings

Achieves a 4p approximation ratio for monotone functions under p-matchoid constraints.

Uses only O(k) memory and O(km/p) queries per element, significantly reducing resource usage.

Outperforms state-of-the-art algorithms by up to fifty times in video summarization tasks.

Abstract

In this paper, we develop the first one-pass streaming algorithm for submodular maximization that does not evaluate the entire stream even once. By carefully subsampling each element of data stream, our algorithm enjoys the tightest approximation guarantees in various settings while having the smallest memory footprint and requiring the lowest number of function evaluations. More specifically, for a monotone submodular function and a $p$-matchoid constraint, our randomized algorithm achieves a $4p$ approximation ratio (in expectation) with $O(k)$ memory and $O(km/p)$ queries per element ($k$ is the size of the largest feasible solution and $m$ is the number of matroids used to define the constraint). For the non-monotone case, our approximation ratio increases only slightly to $4p+2-o(1)$. To the best or our knowledge, our algorithm is the first that combines the benefits of streaming and subsampling in a novel way in order to truly scale submodular maximization to massive machine learning problems. To showcase its practicality, we empirically evaluated the performance of our algorithm on a video summarization application and observed that it outperforms the state-of-the-art algorithm by up to fifty fold, while maintaining practically the same utility.