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We study the online influence maximization problem in social networks under the independent cascade model. Specifically, we aim to learn the set of "best influencers" in a social network online while repeatedly interacting with it. We address the challenges of (i) combinatorial action space, since the number of feasible influencer sets grows exponentially with the maximum number of influencers, and (ii) limited feedback, since only the influenced portion of the network is observed. Under a stochastic semi-bandit feedback, we propose and analyze IMLinUCB, a computationally efficient UCB-based algorithm. Our bounds on the cumulative regret are polynomial in all quantities of interest, achieve near-optimal dependence on the number of interactions and reflect the topology of the network and the activation probabilities of its edges, thereby giving insights on the problem complexity. To the best of our knowledge, these are the first such results. Our experiments show that in several representative graph topologies, the regret of IMLinUCB scales as suggested by our upper bounds. IMLinUCB permits linear generalization and thus is both statistically and computationally suitable for large-scale problems. Our experiments also show that IMLinUCB with linear generalization can lead to low regret in real-world online influence maximization.
Author Information
Zheng Wen (Adobe Research)
Zheng Wen is currently a senior research scientist at Big Data Experience Lab, Adobe Research. His current research focuses on machine learning, operations research, and big data. Before joining Adobe Research, he was a research scientist in Advertising Science Team, Yahoo Labs. Prior to that, he received a Ph.D. in Electrical Engineering from Stanford University.
Branislav Kveton (Adobe Research)
Michal Valko (DeepMind Paris and Inria Lille - Nord Europe)
Michal is a research scientist in DeepMind Paris and SequeL team at Inria Lille - Nord Europe, France, lead by Philippe Preux and Rémi Munos. He also teaches the course Graphs in Machine Learning at l'ENS Cachan. Michal is primarily interested in designing algorithms that would require as little human supervision as possible. This means 1) reducing the “intelligence” that humans need to input into the system and 2) minimising the data that humans need spend inspecting, classifying, or “tuning” the algorithms. Another important feature of machine learning algorithms should be the ability to adapt to changing environments. That is why he is working in domains that are able to deal with minimal feedback, such as semi-supervised learning, bandit algorithms, and anomaly detection. The common thread of Michal's work has been adaptive graph-based learning and its application to the real world applications such as recommender systems, medical error detection, and face recognition. His industrial collaborators include Intel, Technicolor, and Microsoft Research. He received his PhD in 2011 from University of Pittsburgh under the supervision of Miloš Hauskrecht and after was a postdoc of Rémi Munos.
Sharan Vaswani (University of British Columbia)
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2015 Poster: Efficient Thompson Sampling for Online Matrix-Factorization Recommendation »
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