[Paper Review] Adaptive Influence Maximization under General Feedback Models

Guangmo Tong, Ruiqi Wang|arXiv (Cornell University)|Feb 1, 2019

Advanced Bandit Algorithms Research17 references10 citations

TL;DR

This paper introduces a general feedback model for adaptive influence maximization (AIM) where seed nodes are selected at fixed intervals after diffusion rounds, not necessarily after full termination. It proposes the regret ratio as a key metric to analyze the trade-off between waiting for observations and acting early, and provides the first approximation analysis of the greedy policy under non-adaptive-submodular settings, showing a (1−e−1/α(Tg))-approximation bound for the greedy strategy under general feedback models.

ABSTRACT

Influence maximization is a prototypical problem enabling applications in various domains, and it has been extensively studied in the past decade. The classic influence maximization problem explores the strategies for deploying seed users before the start of the diffusion process such that the total influence can be maximized. In its adaptive version, seed nodes are allowed to be launched in an adaptive manner after observing certain diffusion results. In this paper, we provide a systematic study on the adaptive influence maximization problem, focusing on the algorithmic analysis of the scenarios when it is not adaptive submodular. We introduce the concept of regret ratio which characterizes the key trade-off in designing adaptive seeding strategies, based on which we present the approximation analysis for the well-known greedy policy. In addition, we provide analysis concerning improving the efficiencies and bounding the regret ratio. Finally, we propose several future research directions.

Motivation & Objective

• To address the gap in theoretical analysis of adaptive influence maximization (AIM) when the problem is not adaptive submodular under general feedback models.
• To formalize a generalized feedback model that captures real-world constraints like fixed observation intervals and limited observability.
• To introduce the regret ratio as a performance metric that quantifies the trade-off between waiting for observations and seeding early.
• To provide the first approximation analysis of the greedy policy under general feedback models, extending beyond the adaptive submodular regime.
• To explore practical implications and future research directions in adaptive seeding under complex observation constraints.

Proposed method

• Proposes a generalized feedback model where one seed is selected every d diffusion rounds (d ∈ ℤ⁺ ∪ {∞}), generalizing both Myopic (d=1) and Full Adoption (d=∞) models.
• Introduces the regret ratio as a measure of the trade-off between observation quality and seeding timeliness, capturing the cost of not waiting for full diffusion.
• Analyzes the greedy policy using a decision tree framework, deriving a (1−e−1/α(Tg))-approximation bound where α(Tg) quantifies the influence gain per observation.
• Applies the analysis to non-adaptive-submodular settings, extending beyond the standard adaptive submodularity assumption used in prior work.
• Considers extensions to batch-mode seeding and flexible observation models, including limited or probe-based edge observation.
• Models general feedback as a distribution over observable edges from a network state, enabling flexible and realistic observation modeling.

Experimental results

Research questions

• RQ1 How can we theoretically analyze the performance of the greedy policy in adaptive influence maximization when the problem is not adaptive submodular?
• RQ2 What is an effective metric to quantify the trade-off between waiting for more observations and acting early in adaptive seeding?
• RQ3 How does the choice of feedback model (e.g., d=1 vs. d=∞) affect the influence spread and performance of greedy seeding?
• RQ4 Can we bound the approximation ratio of the greedy policy under general feedback models that do not satisfy adaptive submodularity?
• RQ5 What are the implications of limited or flexible observation models on adaptive seeding strategies and their theoretical analysis?

Key findings

• The regret ratio is introduced as a novel metric that captures the fundamental trade-off between observation quality and seeding timeliness in adaptive influence maximization.
• The paper provides the first approximation analysis of the greedy policy under general feedback models that are not adaptive submodular, establishing a (1−e−1/α(Tg))-approximation bound.
• The analysis shows that the greedy policy maintains strong performance even when the problem lacks adaptive submodularity, extending the applicability of greedy methods beyond prior assumptions.
• Experiments demonstrate that adaptive seeding strategies significantly outperform non-adaptive ones in most settings, validating the practical value of the proposed model.
• The general feedback model enables flexible modeling of real-world constraints such as fixed deployment schedules, limited observability, and non-round-based observation triggers.
• The framework generalizes prior models, including Myopic and Full Adoption feedback, and allows for future extensions to probe-based or event-driven observation mechanisms.