Online influence maximization (OIM) is a popular problem in social networks to learn influence propagation model parameters and maximize the influence spread at the same time. Most previous studies focus on the independent cascade (IC) model under the edge-level feedback. In this paper, we address OIM in the linear threshold (LT) model. Because node activations in the LT model are due to the aggregated effect of all active neighbors, it is more natural to model OIM with the nodel-level feedback. And this brings new challenge in online learning since we only observe aggregated effect from groups of nodes and the groups are also random. Based on the linear structure in node activations, we incorporate ideas from linear bandits and design an algorithm $\ltlinucb$ that is consistent with the observed feedback. By proving group observation modulated (GOM) bounded smoothness property, a novel result of the influence difference in terms of the random observations, we provide a regret of order $\tilde{O}(\mathrm{poly}(m)\sqrt{T})$, where $m$ is the number of edges and $T$ is the number of rounds. This is the first theoretical result in such order for OIM under the LT model. In the end, we also provide an algorithm $\oimetc$ with regret bound $O(\mathrm{poly}(m)\ T^{2/3})$, which is model-independent, simple and has less requirement on online feedback and offline computation.

The paper studies the following bandit model: actions are nodes in a known directed graph and at each time step t the following happens: (1) hidden from the player, each edge (i,j) is independently declared "open" or "closed" with fixed but unknown probability w(i,j); (2) the player chooses a subset S_t of nodes of cardinality at most K; (3) all directed paths originated from nodes in S_t that go through open edges are revealed to the player; (4) the player's reward is the number of nodes in these paths. The regret of the player is measured with respect to the expected reward obtained by consistently playing the K-sized subset S of nodes that maximizes the expected reward. Since this set is NP-hard to compute, but easy to approximate, it is assumed that the player has access to an oracle that, given G and estimates of w(i,j) for each edge (i,j), returns the K-sized subset S_t that maximizes the expected reward according to the estimates. The probabilities w(i,j) are assumed to follow a linear model, w(i,j) x(i,j)*theta, where x(i,j) is the known d-dimensional feature vector associated with edge (i,j) and theta is an unknown parameter vector. A special case is the "tabular model" where all the feature vectors are orthogonal.

We study the online influence maximization (OIM) problem in social networks, where the learner repeatedly chooses seed nodes to generate cascades, observes the cascade feedback, and gradually learns the best seeds that generate the largest cascade in multiple rounds. In the demand of the real world, we work with node-level feedback instead of the common edge-level feedback in the literature. The edge-level feedback reveals all edges that pass through information in a cascade, whereas 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. Previously, there is a nearly optimal $\tilde{O}(\sqrt{T})$-regret algorithm for OIM problem under the linear threshold (LT) diffusion model with node-level feedback. It remains unknown whether the same algorithm exists for the independent cascade (IC) diffusion model. In this paper, we resolve this open problem by presenting an $\tilde{O}(\sqrt{T})$-regret algorithm for OIM problem under the IC model with node-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.