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Online Influence Maximization with Semi-Bandit Feedback under Corruptions

Xiaotong Cheng, Behzad Nourani-Koliji, Setareh Maghsudi

TL;DR

This article proposes a novel bandit algorithm, CW-IMLinUCB, which robustly learns and finds the optimal seed set in the presence of corrupted users and establishes that the regret performance of the proposed algorithm is better than the state-of-the-art online influence maximization algorithms.

Abstract

In this work, we investigate the online influence maximization in social networks. Most prior research studies on online influence maximization assume that the nodes are fully cooperative and act according to their stochastically generated influence probabilities on others. In contrast, we study the online influence maximization problem in the presence of some corrupted nodes whose damaging effects diffuse throughout the network. We propose a novel bandit algorithm, CW-IMLinUCB, which robustly learns and finds the optimal seed set in the presence of corrupted users. Theoretical analyses establish that the regret performance of our proposed algorithm is better than the state-of-the-art online influence maximization algorithms. Extensive empirical evaluations on synthetic and real-world datasets also show the superior performance of our proposed algorithm.

Online Influence Maximization with Semi-Bandit Feedback under Corruptions

TL;DR

This article proposes a novel bandit algorithm, CW-IMLinUCB, which robustly learns and finds the optimal seed set in the presence of corrupted users and establishes that the regret performance of the proposed algorithm is better than the state-of-the-art online influence maximization algorithms.

Abstract

In this work, we investigate the online influence maximization in social networks. Most prior research studies on online influence maximization assume that the nodes are fully cooperative and act according to their stochastically generated influence probabilities on others. In contrast, we study the online influence maximization problem in the presence of some corrupted nodes whose damaging effects diffuse throughout the network. We propose a novel bandit algorithm, CW-IMLinUCB, which robustly learns and finds the optimal seed set in the presence of corrupted users. Theoretical analyses establish that the regret performance of our proposed algorithm is better than the state-of-the-art online influence maximization algorithms. Extensive empirical evaluations on synthetic and real-world datasets also show the superior performance of our proposed algorithm.
Paper Structure (17 sections, 4 theorems, 47 equations, 8 figures, 1 table, 1 algorithm)

This paper contains 17 sections, 4 theorems, 47 equations, 8 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. IM Related Work
  4. Bandits with Corruption Related Work
  5. Problem Setup
  6. Notation
  7. Influence Maximization
  8. Online Influence Maximization under Corruption
  9. A Confidence Weighted Bandit Solution
  10. Theoretical Analysis
  11. Experiment
  12. Toy Example
  13. Experiments on Synthetic Dataset
  14. Experiments on Real World Dataset
  15. Conclusion and Discussion
  16. ...and 2 more sections

Key Result

Lemma 1

For any $0 < \delta < 1$ and corruption budget $C \geq 0$, set the confidence radius $\beta = \sigma^{-2}\sqrt{d\log(1+\frac{E^*T}{d}) + 2\log (\frac{1}{\delta})} + \sigma^{-2}\lambda E^cC + \Theta$ then with probability at least $1-\delta$, for every round $t$, the good event $\xi_{t-1} = \{|\bold

Figures (8)

  • Figure 1: Online influence maximization under corruption. Edges between users represent potential pathways for influence propagation. At $t$, when User 1 is activated, all of its out-edges trigger the activation of connected users. However, if User 5 is a corrupted user with unpredictable behavior, the outcomes at $t+1$ can vary. With some unknown probability, User 5 may behave normally (depicted in blue) or act adversarially (depicted in orange). User 5's corrupted behavior does not only perturb the influence diffusion when one selects it as a seed but also interferes with the influence diffusion when Users 1 or 2 are seeds, as user 5 lies within their diffusion pathways.
  • Figure 2: Network structure of Experiment I.
  • Figure 3: Effects of various corrupted user positions ($n = 10$).
  • Figure 4: Effects of various corrupted user positions ($n = 50$).
  • Figure 5: Result of Experiment I.
  • ...and 3 more figures

Theorems & Definitions (20)

  • Remark 1
  • Definition 1: Edge semi-bandit feedback
  • Remark 2
  • Remark 3
  • Remark 4
  • Remark 5
  • Definition 2
  • Lemma 1
  • proof
  • Theorem 1
  • ...and 10 more