LOFA: Online Influence Maximization under Full-Bandit Feedback using Lazy Forward Selection

TL;DR

The paper tackles online Influence Maximization under full-bandit feedback, where at each round a seed set $S^t$ with $|S^t|\le k$ is chosen to maximize the cumulative influence over horizon $T$. It introduces LOFA, a Lazy Online Forward Algorithm that greedily builds seed sets using a lazy-forward mechanism with a max-heap, lazily refreshing marginal gains only when needed to exploit submodularity, and evaluating each exploration arm $m$ times to minimize regret. Empirical results on a real-world Facebook network show LOFA achieves lower empirical regret and higher cumulative rewards than baselines such as DART and ETCG, while maintaining $O(|V|)$ storage and $O(\log|V|)$ per-round time. The work demonstrates how submodularity can be leveraged in online learning to balance exploration and exploitation efficiently, with potential extensions to theoretical regret analysis, scalability, and continuous-impression IM variants.

Abstract

We study the problem of influence maximization (IM) in an online setting, where the goal is to select a subset of nodes$\unicode{x2014}$called the seed set$\unicode{x2014}$at each time step over a fixed time horizon, subject to a cardinality budget constraint, to maximize the expected cumulative influence. We operate under a full-bandit feedback model, where only the influence of the chosen seed set at each time step is observed, with no additional structural information about the network or diffusion process. It is well-established that the influence function is submodular, and existing algorithms exploit this property to achieve low regret. In this work, we leverage this property further and propose the Lazy Online Forward Algorithm (LOFA), which achieves a lower empirical regret. We conduct experiments on a real-world social network to demonstrate that LOFA achieves superior performance compared to existing bandit algorithms in terms of cumulative regret and instantaneous reward.

Figures (6)

• Figure 1: Moving average (window size 100) of instantaneous influence as a function of $t$ for budget $k=4$.
• Figure 2: Moving average (window size 100) of instantaneous influence as a function of $t$ for budget $k=8$.
• Figure 3: Moving average (window size 100) of instantaneous influence as a function of $t$ for budget $k=16$.
• Figure 4: Cumulative regret as a function of time horizon $T$ for budget $k=4$.
• Figure 5: Cumulative regret as a function of time horizon $T$ for budget $k=8$.