[Paper Review] Targeted Advertising on Social Networks Using Online Variational Tensor Regression

Tsuyoshi Idé, Keerthiram Murugesan+2 more|arXiv (Cornell University)|Aug 22, 2022

Tensor decomposition and applications4 citations

TL;DR

This paper proposes TensorUCB, a novel tensor-based contextual bandit framework that models user-product heterogeneity in online targeted advertising via online variational tensor regression. By leveraging multi-mode tensor contexts and mean-field variational inference, it achieves superior influence maximization performance—especially under product diversity—outperforming baselines in cumulative regret and scalability.

ABSTRACT

This paper is concerned with online targeted advertising on social networks. The main technical task we address is to estimate the activation probability for user pairs, which quantifies the influence one user may have on another towards purchasing decisions. This is a challenging task because one marketing episode typically involves a multitude of marketing campaigns/strategies of different products for highly diverse customers. In this paper, we propose what we believe is the first tensor-based contextual bandit framework for online targeted advertising. The proposed framework is designed to accommodate any number of feature vectors in the form of multi-mode tensor, thereby enabling to capture the heterogeneity that may exist over user preferences, products, and campaign strategies in a unified manner. To handle inter-dependency of tensor modes, we introduce an online variational algorithm with a mean-field approximation. We empirically confirm that the proposed TensorUCB algorithm achieves a significant improvement in influence maximization tasks over the benchmarks, which is attributable to its capability of capturing the user-product heterogeneity.

Motivation & Objective

• To address the challenge of influence maximization in online targeted advertising on social networks, where user influence probabilities are unknown and must be learned in real time.
• To model complex heterogeneity across users, products, and marketing strategies in a unified framework that captures interdependencies in multi-dimensional feature spaces.
• To develop a scalable online learning algorithm that integrates probabilistic tensor regression with upper confidence bound (UCB) exploration, enabling efficient and adaptive seed selection.
• To empirically validate that the framework significantly outperforms existing baselines in cumulative regret and influence spread, especially under high product diversity.

Proposed method

• The framework uses a multi-mode tensor (context tensor) to encode user features, product features, and campaign strategy vectors, enabling joint modeling of user-product interactions.
• It applies low-rank CP tensor decomposition to model the activation probability matrix as a function of the context tensor, capturing latent patterns across heterogeneous user and product types.
• An online variational inference algorithm with mean-field approximation is developed to update the posterior distribution of tensor factors in real time, enabling efficient sequential learning.
• The predictive distribution from the tensor regression is used to compute confidence bounds in a UCB-style policy, balancing exploration and exploitation during seed selection.
• The algorithm is formalized as a contextual bandit problem where the 'arm' corresponds to a seed user, the 'context' is the user-product tensor, and the 'reward' is the number of resulting purchases.
• A regret bound analysis is derived based on the closed-form predictive distribution, providing theoretical justification for the algorithm’s performance.

Experimental results

Research questions

• RQ1 Can a tensor-based framework effectively model and generalize over heterogeneous user preferences, product types, and marketing strategies in online advertising?
• RQ2 How does the integration of online variational tensor regression with the UCB policy improve influence maximization compared to existing linear or factorized bandit methods?
• RQ3 What is the impact of tensor rank on performance and regret, particularly in datasets with high product diversity such as Digg?
• RQ4 How does the computational cost of the proposed method scale with graph size and tensor dimensionality, and how does it compare to baselines in practice?

Key findings

• TensorUCB significantly reduces cumulative regret compared to baselines like Random, IMLinUCB, and DILinUCB, especially in high-heterogeneity settings such as the Digg dataset.
• The algorithm outperforms IMFB and COIN in influence spread, even when IMFB is trained on simulated data, demonstrating robustness in real-world data with complex user-product dynamics.
• Increasing the tensor rank R improves regret performance up to a saturation point, validating the model’s ability to capture multiple underlying influence patterns across users and products.
• Computation time per round scales linearly with graph size, making TensorUCB efficient and practical for large-scale social networks, with performance comparable to IMLinUCB but with far better regret reduction.
• The framework maintains stable performance across diverse datasets (Flixster and Digg), showing resilience to data sparsity and varying levels of product category heterogeneity.
• The integration of tensor-based context modeling with UCB enables better generalization than feature-agnostic or linear bandit baselines, particularly when product-specific diffusion dynamics vary significantly.