Online Contextual Influence Maximization in social networks

Abstract

Abstract-In this paper, we propose the Online Contextual Influence Maximization Problem (OCIMP). In OCIMP, the learner faces a series of epochs in each of which a different influence campaign is run to promote a certain product in a given social network. In each epoch, the learner first distributes a limited number of free-samples of the product among a set of seed nodes in the social network. Then, the influence spread process takes place over the network, other users get influenced and purchase the product. The goal of the learner is to maximize the expected total number of influenced users over all epochs. We depart from the prior work in two aspects: (i) the learner does not know how the influence spreads over the network, i.e., it is unaware of the influence probabilities; (ii) influence probabilities depend on the context. We develop a learning algorithm for OCIMP, called Contextual Online INfluence maximization (COIN). COIN can use any approximation algorithm that solves the offline influence maximization problem as a subroutine to obtain the set of seed nodes in each epoch. When the influence probabilities are Hölder continuous functions of the context, we prove that COIN achieves sublinear regret with respect to an approximation oracle that knows the influence probabilities for all contexts. Moreover, our regret bound holds for any sequence of contexts. We also test the performance of COIN on several social networks, and show that it performs better than other methods.

Online Contextual Influence Maximization With Costly Observations

“…The set of influenced nodes is not freely revealed to the learner at the end of an epoch. 1 We will compare the performance of the learner with the performance of an oracle that knows the influence probabilities perfectly. For this, we define below the omnipotent oracle.…”

“…As observed from Theorem 3, COIN-CO-EL explores less when the cost of observation is large. In addition, when the cost is 0, the regret bound is equivalent to the regret bound in [1], which does not consider the observation costs and assumes that the influence outcomes are always observed. This result shows that sublinear number of observations is sufficient to achieve the same order of regret as in [1].…”

“…1) Cost-free Edge-level Feedback: In this setting, the influence outcomes on all edges with activation attempts are observed at the end of each epoch with no cost (c = 0). This is the setting that is proposed in our prior work [1].…”

“…To the best of our knowledge, none of the prior works in topic-aware IM develop learning algorithms with provable performance guarantees for the case when the influence probabilities are unknown. In addition, prior works in IM that consider unknown influence probabilities do not consider the cost of feedback (cost of observation of the influence spread process) [1], [15]- [18]. However, this cost exists in most of the real-world applications of IM.…”

Combinatorial multi-armed bandit problem with probabilistically triggered arms: A case with bounded regret

“…In this problem, the seed set corresponds to the action, edges of the network correspond to arms, the influence spread corresponds to the reward, and the ATPs are determined by an influence spread process. Various works consider the online version of this problem, named the OIM problem (Lei et al, 2015;Vaswani et al, 2015;Wen et al, 2017;Sarıtaç et al, 2016). In this version, the ATPs are unknown a priori.…”