[Paper Review] No Time to Observe: Adaptive Influence Maximization with Partial Feedback

Jing Yuan, Shaojie Tang|arXiv (Cornell University)|Sep 1, 2016

Advanced Bandit Algorithms Research13 references3 citations

TL;DR

This paper introduces a novel partial-feedback model for adaptive influence maximization that balances performance and delay by allowing seed selection at intermediate stages of diffusion. It proposes two greedy policies—$π^\beta$ and $\pi^{\beta-\text{enhanced}}$—that achieve bounded approximation ratios under both uniform and non-uniform cost settings, with theoretical guarantees up to $(1-e^{-1})/2$ under full feedback.

ABSTRACT

Although influence maximization problem has been extensively studied over the past ten years, majority of existing work adopt one of the following models: \emph{full-feedback model} or \emph{zero-feedback model}. In the zero-feedback model, we have to commit the seed users all at once in advance, this strategy is also known as non-adaptive policy. In the full-feedback model, we select one seed at a time and wait until the diffusion completes, before selecting the next seed. Full-feedback model has better performance but potentially huge delay, zero-feedback model has zero delay but poorer performance since it does not utilize the observation that may be made during the seeding process. To fill the gap between these two models, we propose \emph{Partial-feedback Model}, which allows us to select a seed at any intermediate stage. We develop two novel greedy policies that, for the first time, achieve bounded approximation ratios under both uniform and non-uniform cost settings.

Motivation & Objective

• To address the performance-delay tradeoff in influence maximization by introducing a generalized partial-feedback model.
• To develop adaptive policies that achieve bounded approximation ratios under partial feedback, where full feedback is not available but some intermediate observations are possible.
• To overcome the challenge that influence under partial feedback is not adaptive submodular, a key limitation in prior adaptive submodular optimization.
• To provide theoretical guarantees for greedy policies in settings where feedback is incomplete but timely, enabling practical deployment in time-critical viral marketing.

Proposed method

• Proposes a partial-feedback model that allows seed selection at any intermediate stage, bridging the gap between zero-feedback (non-adaptive) and full-feedback (adaptive) models.
• Introduces a greedy policy $\pi^\beta$ that selects seeds based on a control parameter $\beta$, balancing exploration and exploitation over time.
• Develops an enhanced greedy policy $\pi^{\beta-\text{enhanced}}$ that combines $\pi^\beta$ with a random choice of the top single-node seed to improve performance.
• Uses Monte Carlo simulations to estimate influence spread, with edge propagation probabilities drawn from $i \times \{0.01, 0.001\}$, as in prior work.
• Employs theoretical analysis to prove bounded approximation ratios, leveraging submodularity and adaptive submodularity concepts.
• Applies the independent cascade (IC) model to model diffusion dynamics, with each node having a cost and each edge a propagation probability.

Experimental results

Research questions

• RQ1 Can we design adaptive influence maximization policies that achieve bounded approximation ratios under partial feedback, where only partial observations of diffusion are available during seeding?
• RQ2 How does the performance of adaptive seeding under partial feedback compare to non-adaptive (zero-feedback) and full-feedback policies in terms of influence spread and delay?
• RQ3 What is the impact of the control parameter $\alpha$ (or $\beta$) on the tradeoff between delay and influence spread in the partial-feedback model?
• RQ4 Can we overcome the non-adaptive submodularity of the objective function under partial feedback to still achieve theoretical performance guarantees?
• RQ5 How does edge propagation probability affect the benefit of partial feedback in real-world networks?

Key findings

• The enhanced greedy policy $\pi^{\beta-\text{enhanced}}$ achieves an approximation ratio of $\frac{(1-e^{-\beta})}{2}f(\pi^*)$, with a guaranteed lower bound of $\frac{(1-e^{-1})}{2}f(\pi^*)$ under full feedback.
• On the NetHEPT dataset, with $i=4$ and budget 50, partial feedback ($\alpha=0.8$) increased influence spread from 57 (zero-feedback) to 87, a 52.6% improvement.
• With $i=2$, a $10\%$ improvement in influence spread was achieved at $\alpha=0.6$, and with $i=4$, a $20\%$ improvement was seen at $\alpha=0.4$, showing strong gains under moderate propagation probabilities.
• The benefit of partial feedback becomes more pronounced as edge propagation probabilities increase, indicating that uncertainty in diffusion outcomes amplifies the value of intermediate observations.
• When edge propagation probabilities are low (e.g., $i=1$), the advantage of partial feedback is minimal, as sampling-based estimates already closely match actual outcomes.
• The proposed policies effectively balance delay and performance by adjusting the control parameter $\alpha$, enabling practical deployment in time-sensitive applications.