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arxiv: 2604.19672 · v1 · submitted 2026-04-21 · 💻 cs.LG · stat.ML

Recognition: unknown

Budgeted Online Influence Maximization

Pierre Perrault , Jennifer Healey , Zheng Wen , Michal Valko
Authors on Pith no claims yet

Pith reviewed 2026-05-10 03:36 UTC · model grok-4.3

classification 💻 cs.LG stat.ML
keywords online influence maximizationbudget constraintindependent cascade modelsemi-bandit feedbackregret boundsonline learningsocial advertising
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The pith

A budgeted framework for online influence maximization replaces fixed influencer counts with total cost limits and improves regret bounds.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shifts online influence maximization from a cardinality constraint on the number of selected influencers to a total budget constraint on their varying costs. This change directly models real advertising campaigns where the goal is maximum spread for a fixed spend rather than a fixed headcount. The authors develop an algorithm under the independent cascade diffusion model that operates with edge-level semi-bandit feedback, learning which edges activate after each selection. They derive theoretical regret bounds for the budgeted setting and prove that the same analysis yields a stricter bound than prior work when restricted to the cardinality case. A reader cares because the budgeted view aligns with actual budget allocation decisions and delivers stronger performance guarantees even in the classic setting.

Core claim

We introduce a new budgeted framework for online influence maximization, considering the total cost of an advertising campaign instead of the common cardinality constraint on a chosen influencer set. Our approach better models the real-world setting where the cost of influencers varies and advertisers want to find the best value for their overall social advertising budget. We propose an algorithm assuming an independent cascade diffusion model and edge level semi-bandit feedback, and provide both theoretical and experimental results. Our analysis is also valid for the cardinality constraint setting and improves the state of the art regret bound in this case.

What carries the argument

Budgeted online influence maximization algorithm under the independent cascade model with edge-level semi-bandit feedback, which selects seeds while tracking cumulative cost against the budget and updates estimates from observed edge activations.

If this is right

  • Advertisers can select influencers online while respecting a hard monetary budget instead of a preset number of seeds.
  • Regret guarantees hold in the budgeted setting and carry over to improve prior bounds under cardinality constraints.
  • Experimental validation on both synthetic and real networks confirms that the algorithm learns effective selections from partial edge observations.
  • The same semi-bandit feedback model supports analysis for both budgeted and non-budgeted variants without changing the core proof structure.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The budgeted formulation opens the door to treating influencer selection as a knapsack-style resource allocation problem inside online learning loops.
  • If real campaigns supply cost data and edge-level observations, the framework could be deployed directly on live platforms to test return on ad spend.
  • Extensions to other diffusion models would require only that the semi-bandit feedback assumption still yields unbiased estimates of activation probabilities.

Load-bearing premise

The spread of influence follows the independent cascade model and the learner observes which edges activate after each seed selection.

What would settle it

A controlled experiment on a social graph with heterogeneous node costs that runs the budgeted algorithm against a cardinality baseline under identical total spend and measures whether the budgeted version produces strictly lower cumulative regret or lower final influence spread; sustained underperformance would falsify the claimed improvement.

Figures

Figures reproduced from arXiv: 2604.19672 by Jennifer Healey, Michal Valko, Pierre Perrault, Zheng Wen.

Figure 1
Figure 1. Figure 1: Regret curves with respect to the budget B (expectation computed by averaging over 10 independent simulations). In this section, we present an experiment for Budgeted OIM. In [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Regret curves on five different problem instances, with respect to the budget B (expectation computed by averaging over 10 independent simulations). maximize the function σ while minimizing the cost function. The fundamental difference is on the importance given to one or the other function, controled by λ. We use a greedy maximization in BOIM-CUCB-REGULARIZED. A greedy optimization of the objective S 7→ σ… view at source ↗
read the original abstract

We introduce a new budgeted framework for online influence maximization, considering the total cost of an advertising campaign instead of the common cardinality constraint on a chosen influencer set. Our approach better models the real-world setting where the cost of influencers varies and advertisers want to find the best value for their overall social advertising budget. We propose an algorithm assuming an independent cascade diffusion model and edge level semi-bandit feedback, and provide both theoretical and experimental results. Our analysis is also valid for the cardinality constraint setting and improves the state of the art regret bound in this case.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 1 minor

Summary. The paper introduces a budgeted variant of online influence maximization where the constraint is on the total advertising cost rather than the cardinality of the seed set. It proposes an algorithm under the independent cascade model with edge-level semi-bandit feedback, derives theoretical regret bounds, and reports experimental results. The analysis is claimed to extend to the standard cardinality-constrained setting while improving upon the state-of-the-art regret bound.

Significance. If the regret bounds are valid under the stated assumptions, the budgeted formulation addresses a more realistic modeling gap in online IM. The extension to cardinality and the claimed regret improvement would strengthen the contribution, provided the comparison accounts for differences in feedback models. Experimental validation adds empirical weight, though its robustness depends on the details of the setup.

major comments (1)
  1. [Abstract and theoretical analysis] Abstract and theoretical analysis section: The claim that the analysis 'improves the state of the art regret bound' in the cardinality-constraint setting must be supported by an explicit comparison under matched feedback assumptions. Prior OIM regret analyses often use node-level or set-level feedback; if the new bound relies on the stronger edge-level semi-bandit observations, it does not constitute a strict improvement and the paper should state the feedback model of each cited baseline.
minor comments (1)
  1. [Abstract] The abstract would benefit from a brief statement of the achieved regret bound (e.g., O(·) dependence) to allow readers to assess the improvement magnitude without reading the full proofs.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive feedback. We address the major comment on clarifying the regret bound comparison under matched feedback assumptions and will revise the manuscript to improve transparency.

read point-by-point responses

  1. Referee: [Abstract and theoretical analysis] Abstract and theoretical analysis section: The claim that the analysis 'improves the state of the art regret bound' in the cardinality-constraint setting must be supported by an explicit comparison under matched feedback assumptions. Prior OIM regret analyses often use node-level or set-level feedback; if the new bound relies on the stronger edge-level semi-bandit observations, it does not constitute a strict improvement and the paper should state the feedback model of each cited baseline.

    Authors: We agree that an explicit comparison under matched feedback assumptions is required to support the improvement claim. Our analysis and algorithm are developed for the edge-level semi-bandit feedback model, which provides per-edge activation observations and is stronger than the node-level or set-level feedback used in several prior OIM works. In the revised manuscript we will add a comparison table (in the theoretical analysis or related work section) that explicitly lists the feedback model and regret bound for each cited baseline. We will also revise the abstract and analysis text to state the feedback assumptions of the baselines and qualify our claim as an improvement within the edge-level semi-bandit setting. This change ensures the positioning of our contribution is accurate and transparent. revision: yes

Circularity Check

0 steps flagged

No circularity; bounds derived from IC model and semi-bandit feedback assumptions

full rationale

The paper introduces a budgeted online IM framework under the independent cascade diffusion model with edge-level semi-bandit feedback. The algorithm and regret analysis are presented as derived from these modeling choices, with an extension to the cardinality-constraint case that claims an improved bound. No self-definitional reductions, fitted parameters renamed as predictions, or load-bearing self-citations appear in the provided abstract and description. The central claims rest on standard diffusion assumptions and the new budgeted setting rather than tautological equivalence to inputs. The skeptic concern about feedback-model mismatch is a question of comparative validity, not a circularity in the derivation chain itself.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the independent cascade model as a domain assumption and edge-level semi-bandit feedback; no free parameters or invented entities are specified in the abstract.

axioms (1)
  • domain assumption Independent cascade diffusion model
    Standard model for influence spread assumed for the diffusion process.

pith-pipeline@v0.9.0 · 5380 in / 1019 out tokens · 48450 ms · 2026-05-10T03:36:16.469442+00:00 · methodology

discussion (0)

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