Title: Streaming Stochastic Submodular Maximization with On-Demand User Requests
Venue: NeurIPS 2025
Accepted: yes
Keywords: Streaming

Submodular Maximization

Stochastic Algorithms

Coverage

User Request
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 web\-site at any time, and upon each visit, 
the web\-site 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 $1/8\delta$,  where $\delta$ 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.


Peer reviews:
comments: SUMMARY:
This paper aims at a  streaming submodular maximization.  The context is that a user can visit a site and the site needs to present k distinct items to the users. These items will be consumed with a fixed probability (per item) which each item represents some topics. The goal is to design a streaming algorithm that maximizes the expected total topic coverage. 

The authors show that this problem can be formulated as a submodular maximization subject to a matroid constraint under an ideal case:   the number of user visits is known in advance or linear-size memory in the stream length is available.

To do away from these assumptions, the authors proposed another streaming algorithm that achieves a competitive ratio of 1/8\delta, where \delta controls the approximation quality.

STRENGTHS AND WEAKNESSES:
The strength of this paper is in discovering the "connection" with the submodular maximization.

The authors also provide a cute approximation algorithm which can achieve 1/8\delta, competitive ratio.

The presentation, in particular, on Section 3, can be improved since there are a lot of claims that need formal proof but I guess it is due to the page limit that the authors didn't put the proof in the main text.

Overall, I enjoy reading the paper.

QUESTIONS:
Overall, it is a piece of work that introduces a good approximation algorithm, and it has performance guarantees.

I enjoy reading the paper.

LIMITATIONS:
N.A.
TITLE: Official Review
CLARITY: 3
IMPACT: 3
ORIGINALITY: 3
DATE: 2025-06-27

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper investigates a novel variant of the streaming submodular maximization problem. The authors consider a setting in which users may visit a news website at any time, and upon each visit, the website must display up to $k$ news items. Each news item covers a subset of topics and has a certain probability of being clicked by the user. The objective is to design a streaming algorithm that maximizes the expected total topic coverage. To address this, the authors draw a connection to submodular maximization under a matroid constraint.\n\nSTRENGTHS AND WEAKNESSES:\nThe paper introduces a new variant of the streaming submodular maximization problem and proposes memory- and time-efficient algorithms to address it. However, I have several concerns about both the problem setting and the technical contributions:\n\n1. The paper uses news recommendation as a motivating example, focusing on the development of memory-efficient online algorithms that avoid storing all incoming news items. While this may be reasonable for serving a single user, real-world news platforms typically serve a large number of users. To provide near-optimal recommendations across all users, storing all news items may still be necessary. For instance, if the proposed algorithm is applied independently to each user, the union of the candidate sets across all users could approximate the full set of news items, especially given users' diverse preferences. This observation challenges the practicality of the memory savings claimed by the authors.\n\n2. It is unclear what concrete advantages the proposed algorithms offer over existing methods such as LMGreedy. In particular, the memory requirement of their algorithm depends on $T'$, an upper bound on $T$ (the number of visits). In the worst case, $T'$ could be as large as $N$, the total number of news items. In such scenarios, the proposed method may offer little to no improvement over baseline approaches—unless it is shown to be robust to inaccurate estimates of $T$, which is not thoroughly addressed in the paper.\n\nQUESTIONS:\nPlease see weakness section for my concerns regarding both the problem setting and technical contribution.\n\nLIMITATIONS:\nYes.", "TITLE": "Official Review", "RECOMMENDATION": 3, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-07-01"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper introduces the steaming stochastic submodular maximization with on-demand requests (S3MOR) problem, motivated by online news recommendation systems. The goal is to select $T$ news sets (corresponding to $T$ user visits) that maximize the expected number of topics covered. This problme is further formalized as monotone submodular maximization problem under a matroid constraint.\n\nThe main contribution are three approximation algorithms:\n- Given sufficient memory, a 1/2-approximation algorithm is proposed with $\\Omega(N+kT)$ memory usage and  $O(NTk)$ running time.\n- To improve the memory usage, a $\\frac{1}{4(T'-T+1)}$-approxiamtion algorithm is proposed with $O(T'k)$ memory usage and  $O(NT'k)$ running time, where $T'$ is a given upper bound to the number of user accesses $T$.\n- To further achieve a constant approximation ratio, a $1/(8\\delta)$-approximation algorithm is proposed with $O(T'^2k/\\delta)$ memory usage and  $O(NT'^2k/delta)$ running time.\n\nThe empirical evaluation shows the proposed algorithms consistently outperform the baselines regarding function value, runtime and memory.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths\n- The paper introduces an interesting online setting for streaming submodular maximization problems, capturing real-world challenges in online news recommendations. It models the goal of maximizing topic coverage while adapting to dynamic user visits, making it applicable to recommendation systems that aim to diversify content exposure. \n- The authors propose three progressively refined approximation algorithms with different trade-offs between accuracy and memory efficiency. \n- The paper includes extensive experiments on six real-world datasets, validating the effectiveness of the proposed methods. The results demonstrate that the algorithms outperform baselines in terms of objective value (topic coverage), runtime efficiency, and memory consumption.\n- The paper is well-structured and clearly written, making it accessible to readers.\nThe logical flow from problem formulation to theoretical analysis and empirical evaluation enhances readability.\n\nWeaknesses\n- The probability $p_i$ that the user clicks an item $i$ is not clearly explained before the formal problem definition (Problem 2.2). It remains unclear whether click probabilities remain static or evolve based on user behavior over time.\n- The paper does not discuss how to estimate the total number of user visits $T$. Under the streaming setting, the predefined $T'$ sets may become insufficient if users continue visiting beyond expectations. The experimental setup assumes prior knowledge of T, which may not be realistic. The author may need to either add a discussion on how to guess $T$ and implement it in the experiment or add an assumption to $T$.\n\nQUESTIONS:\n- Line 16: The range of $\\delta$ should be provided. Otherwise, it could be misleading that the approximation ratio could be better than $1/8$. Also, add parenthesis as $1/(8\\delta)$\n- Table 1: On line 182, it is discussed that the memory usage of LMGreedy is $\\Omega(N+kT)$. However, it is listed as $O(N+kT)$ in the table.\n- Line 224: Does $f_{\\cup_{t\\in [T']} \\mathcal A^t}(V_j)$ represents the marginal gain?\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-02"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis work introduces and studies a new problem in streaming submodular maximization, called Streaming Stochastic Submodular Maximization with On-demand Requests, or S3MOR in short. This problem is motivated by the setting of wanting to diversify the news feed of a user, where the news coverage goes up only if the user actually clicks on an item. Formally, there is a stream $\\mathcal{V} = \\{V_1,\\dots,\\}$ of news items, and each item $V_i$ covers a subset of topics from a given universe of topics $C = \\{c_1,\\dots,c_d\\}$. The problem solver is given each news item tagged with a value $p_i$ that is the probability that the item will be clicked on. Further, at every time step $i$, a binary variable $\\tau_i \\in \\{0,1\\}$ is observed indicating whether or not the user of interest is online or not; if $\\tau_i = 1$ then the solver must pick some at most $k$ items from $\\{V_1,\\dots,V_i\\}$ to maximize the topic coverage for the user. The quality of the solvers algorithm is measured as the expected number of topics covered over the course of the stream.\n\nAfter introducing this problem, the authors establish a baseline by showing that this can be reduced to submodular maximization under a partition matroid constraint, and so by storing the entire data stream and applying a batch algorithm, they achieve a $1/2$ approximation - they call this algorithm LMGreedy. It is known that it is not possible to achieve better than a $1/2$ approximation in the worst case setting for streaming submodular maximization, but the downside of LMGreedy is its high memory usage.\n\nSo as to address this issue, the authors construct memory efficient streaming algorithms. One technical issue they come across is that their first method (STORM) achieves a good approximation of $1/4$ only when the number of visits made by the user is known in advance, and degrades reciprocally with the gap between the known upper bound on the number of visits and the number of visits actually made. To address this, they adopt an adaptive approach where they initialize a sequence of guesses for the number of visits by the users and adapt to the sequence. This allows them to interpolate smoothly by achieving an approximation factor of $1/8\\delta$ for any fixed parameter $\\delta\\in\\mathbb{N}$, and achieve space complexity $O(T'^2k/\\delta)$ and time complexity $O(NkT'^2/\\delta)$, where $T'$ is the actual number of times the user visits.\n\nFinally, the authors conduct some experiments demonstrating that their methods do indeed allow one to trade off coverage and space/time complexity effectively.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n1. The paper is well-written and easy to understand.\n2. The treatment of the problem is comprehensive with reasonable theoretical results and experimental corroboration.\n\nWeaknesses:\n1. I think this work is reasonably interesting but maybe not very novel. Based on the problem description and the technical description, although S3MOR seems reasonably posed there are some aspects of the problem description which needs more elaboration. Why is it reasonable to assume we have a clean probability tag for each item, and how would this perform under misspecification? How does this compare to other algorithms in the streaming submodular maximization literature which maybe don't exactly match this problem description but can perhaps still be applied?\n\nQUESTIONS:\n1. Could you please address what I've written in the Weaknesses section above?\n2. In your experiments, how did you generate your $p_i$ values to run your experiments?\n\nLIMITATIONS:\nI think I've address any issues I have with limitations above in the Weaknesses section.", "TITLE": "Official Review", "RECOMMENDATION": 3, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-07-03"}