Streaming Stochastic Submodular Maximization with On-Demand User Requests

TL;DR

This work introduces S3MOR, a streaming framework for stochastic submodular maximization with on-demand user visits, motivated by news recommendations. By reducing S3MOR to submodular maximization under a partition matroid, it leverages existing online streaming algorithms and derives a spectrum of memory-limited solutions. LMGreedy attains the best possible 1/2 competitive ratio when the entire stream can be stored, while Storm and Storm++ enable single-pass, memory-bounded guarantees with competitive ratios of 1/4(T'-T+1) and 1/(8δ), respectively. Empirical results on six real-world datasets show that the proposed methods consistently outperform baselines in both coverage quality and efficiency, highlighting practical viability for on-demand, diverse content recommendation under streaming constraints.

Abstract

We explore a novel problem in streaming submodular maximization, inspired by the dynamics of news-recommendation platforms. We consider a setting where users can visit a news website at any time, and upon each visit, the website must display up to $k$ news items. User interactions are inherently stochastic: each news item presented to the user is consumed with a certain acceptance probability by the user, and each news item covers certain topics. Our goal is to design a streaming algorithm that maximizes the expected total topic coverage. To address this problem, we establish a connection to submodular maximization subject to a matroid constraint. We show that we can effectively adapt previous methods to address our problem when the number of user visits is known in advance or linear-size memory in the stream length is available. However, in more realistic scenarios where only an upper bound on the visits and sublinear memory is available, the algorithms fail to guarantee any bounded performance. To overcome these limitations, we introduce a new online streaming algorithm that achieves a competitive ratio of $1/(8δ)$, where $δ$ controls the approximation quality. Moreover, it requires only a single pass over the stream, and uses memory independent of the stream length. Empirically, our algorithms consistently outperform the baselines.

Figures (18)

• Figure 1: Schematic view of our algorithm Storm. We first initialize $T\xspace'\xspace$ empty active candidate sets. For each incoming news item in the stream $\mathbf{S}$, we decide whether it can be added to/swapped into each of the active candidate sets. When a user submits a request, i.e., $\tau\xspace_j = 1$, we select the best active candidate set, present it to the user, and deactivate it.
• Figure 2: Empirical variation in expected coverage as a function of budget $k$ on all datasets. Parameter $T = 5$, $\delta = 25$ and $\Delta T\xspace = 45$ are fixed
• Figure 3: Empirical variation in expected coverage as a function of number of visits $T\xspace$ on all datasets. Parameter $k = 10$, $\delta = 10$ and $\Delta T\xspace = 10$ are fixed.
• Figure 4:
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Theorems & Definitions (18)

• Lemma 2.0
• Theorem 2.3
• Theorem 3.1
• Theorem 3.2
• Definition A.1: Matroid
• Definition A.2: Partition matroid
• Lemma B.0
• proof
• Theorem B.1
• proof