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Register a new userOnline Influence Maximization under Independent Cascade Model with Semi-Bandit Feedback
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Zheng Wen
Publication date
2016
fields
Informatics Engineering
and research's language is
English
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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.
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We study a novel variant of online finite-horizon Markov Decision Processes with adversarially changing loss functions and initially unknown dynamics. In each episode, the learner suffers the loss accumulated along the trajectory realized by the policy chosen for the episode, and observes aggregate bandit feedback: the trajectory is revealed along with the cumulative loss suffered, rather than the individual losses encountered along the trajectory. Our main result is a computationally efficient algorithm with $O(sqrt{K})$ regret for this setting, where $K$ is the number of episodes. We establish this result via an efficient reduction to a novel bandit learning setting we call Distorted Linear Bandits (DLB), which is a variant of bandit linear optimization where actions chosen by the learner are adversarially distorted before they are committed. We then develop a computationally-efficient online algorithm for DLB for which we prove an $O(sqrt{T})$ regret bound, where $T$ is the number of time steps. Our algorithm is based on online mirror descent with a self-concordant barrier regularization that employs a novel increasing learning rate schedule.
We propose a detailed analysis of the online-learning problem for Independent Cascade (IC) models under node-level feedback. These models have widespread applications in modern social networks. Existing works for IC models have only shed light on edge-level feedback models, where the agent knows the explicit outcome of every observed edge. Little is known about node-level feedback models, where only combined outcomes for sets of edges are observed; in other words, the realization of each edge is censored. This censored information, together with the nonlinear form of the aggregated influence probability, make both parameter estimation and algorithm design challenging. We establish the first confidence-region result under this setting. We also develop an online algorithm achieving a cumulative regret of $mathcal{O}( sqrt{T})$, matching the theoretical regret bound for IC models with edge-level feedback.
We study the problem of online influence maximization in social networks. In this problem, a learner aims to identify the set of best influencers in a network by interacting with it, i.e., repeatedly selecting seed nodes and observing activation feedback in the network. We capitalize on an important property of the influence maximization problem named network assortativity, which is ignored by most existing works in online influence maximization. To realize network assortativity, we factorize the activation probability on the edges into latent factors on the corresponding nodes, including influence factor on the giving nodes and susceptibility factor on the receiving nodes. We propose an upper confidence bound based online learning solution to estimate the latent factors, and therefore the activation probabilities. Considerable regret reduction is achieved by our factorization based online influence maximization algorithm. And extensive empirical evaluations on two real-world networks showed the effectiveness of our proposed solution.
We study the online influence maximization (OIM) problem in social networks, where in multiple rounds the learner repeatedly chooses seed nodes to generate cascades, observes the cascade feedback, and gradually learns the best seeds that generate the largest cascade. We focus on two major challenges in this paper. First, we work with node-level feedback instead of edge-level feedback. The edge-level feedback reveals all edges that pass through information in a cascade, where the node-level feedback only reveals the activated nodes with timestamps. The node-level feedback is arguably more realistic since in practice it is relatively easy to observe who is influenced but very difficult to observe from which relationship (edge) the influence comes from. Second, we use standard offline oracle instead of offline pair-oracle. To compute a good seed set for the next round, an offline pair-oracle finds the best seed set and the best parameters within the confidence region simultaneously, and such an oracle is difficult to compute due to the combinatorial core of OIM problem. So we focus on how to use the standard offline influence maximization oracle which finds the best seed set given the edge parameters as input. In this paper, we resolve these challenges for the two most popular diffusion models, the independent cascade (IC) and the linear threshold (LT) model. For the IC model, the past research only achieves edge-level feedback, while we present the first $widetilde{O}(sqrt{T})$-regret algorithm for the node-level feedback. Besides, the algorithm only invokes standard offline oracles. For the LT model, a recent study only provides an OIM solution that meets the first challenge but still requires a pair-oracle. In this paper, we apply a similar technique as in the IC model to replace the pair-oracle with a standard oracle while maintaining $widetilde{O}(sqrt{T})$-regret.
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