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Register a new userFair Influence Maximization: A Welfare Optimization Approach
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Shahin Jabbari
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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Several behavioral, social, and public health interventions, such as suicide/HIV prevention or community preparedness against natural disasters, leverage social network information to maximize outreach. Algorithmic influence maximization techniques have been proposed to aid with the choice of peer leaders or influencers in such interventions. Yet, traditional algorithms for influence maximization have not been designed with these interventions in mind. As a result, they may disproportionately exclude minority communities from the benefits of the intervention. This has motivated research on fair influence maximization. Existing techniques come with two major drawbacks. First, they require committing to a single fairness measure. Second, these measures are typically imposed as strict constraints leading to undesirable properties such as wastage of resources. To address these shortcomings, we provide a principled characterization of the properties that a fair influence maximization algorithm should satisfy. In particular, we propose a framework based on social welfare theory, wherein the cardinal utilities derived by each community are aggregated using the isoelastic social welfare functions. Under this framework, the trade-off between fairness and efficiency can be controlled by a single inequality aversion design parameter. We then show under what circumstances our proposed principles can be satisfied by a welfare function. The resulting optimization problem is monotone and submodular and can be solved efficiently with optimality guarantees. Our framework encompasses as special cases leximin and proportional fairness. Extensive experiments on synthetic and real world datasets including a case study on landslide risk management demonstrate the efficacy of the proposed framework.
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The influence maximization (IM) problem aims at finding a subset of seed nodes in a social network that maximize the spread of influence. In this study, we focus on a sub-class of IM problems, where whether the nodes are willing to be the seeds when being invited is uncertain, called contingency-aware IM. Such contingency aware IM is critical for applications for non-profit organizations in low resource communities (e.g., spreading awareness of disease prevention). Despite the initial success, a major practical obstacle in promoting the solutions to more communities is the tremendous runtime of the greedy algorithms and the lack of high performance computing (HPC) for the non-profits in the field -- whenever there is a new social network, the non-profits usually do not have the HPCs to recalculate the solutions. Motivated by this and inspired by the line of works that use reinforcement learning (RL) to address combinatorial optimization on graphs, we formalize the problem as a Markov Decision Process (MDP), and use RL to learn an IM policy over historically seen networks, and generalize to unseen networks with negligible runtime at test phase. To fully exploit the properties of our targeted problem, we propose two technical innovations that improve the existing methods, including state-abstraction and theoretically grounded reward shaping. Empirical results show that our method achieves influence as high as the state-of-the-art methods for contingency-aware IM, while having negligible runtime at test phase.
Uncertainty about models and data is ubiquitous in the computational social sciences, and it creates a need for robust social network algorithms, which can simultaneously provide guarantees across a spectrum of models and parameter settings. We begin an investigation into this broad domain by studying robust algorithms for the Influence Maximization problem, in which the goal is to identify a set of k nodes in a social network whose joint influence on the network is maximized. We define a Robust Influence Maximization framework wherein an algorithm is presented with a set of influence functions, typically derived from different influence models or different parameter settings for the same model. The different parameter settings could be derived from observed cascades on different topics, under different conditions, or at different times. The algorithms goal is to identify a set of k nodes who are simultaneously influential for all influence functions, compared to the (function-specific) optimum solutions. We show strong approximation hardness results for this problem unless the algorithm gets to select at least a logarithmic factor more seeds than the optimum solution. However, when enough extra seeds may be selected, we show that techniques of Krause et al. can be used to approximate the optimum robust influence to within a factor of 1 - 1/e. We evaluate this bicriteria approximation algorithm against natural heuristics on several real-world data sets. Our experiments indicate that the worst-case hardness does not necessarily translate into bad performance on real-world data sets; all algorithms perform fairly well.
We consider transferable-utility profit-sharing games that arise from settings in which agents need to jointly choose one of several alternatives, and may use transfers to redistribute the welfare generated by the chosen alternative. One such setting is the Shared-Rental problem, in which students jointly rent an apartment and need to decide which bedroom to allocate to each student, depending on the students preferences. Many solution concepts have been proposed for such settings, ranging from mechanisms without transfers, such as Random Priority and the Eating mechanism, to mechanisms with transfers, such as envy free solutions, the Shapley value, and the Kalai-Smorodinsky bargaining solution. We seek a solution concept that satisfies three natural properties, concerning efficiency, fairness and decomposition. We observe that every solution concept known (to us) fails to satisfy at least one of the three properties. We present a new solution concept, designed so as to satisfy the three properties. A certain submodularity condition (which holds in interesting special cases such as the Shared-Rental setting) implies both existence and uniqueness of our solution concept.
Social networks have been popular platforms for information propagation. An important use case is viral marketing: given a promotion budget, an advertiser can choose some influential users as the seed set and provide them free or discounted sample products; in this way, the advertiser hopes to increase the popularity of the product in the users friend circles by the world-of-mouth effect, and thus maximizes the number of users that information of the production can reach. There has been a body of literature studying the influence maximization problem. Nevertheless, the existing studies mostly investigate the problem on a one-off basis, assuming fixed known influence probabilities among users, or the knowledge of the exact social network topology. In practice, the social network topology and the influence probabilities are typically unknown to the advertiser, which can be varying over time, i.e., in cases of newly established, strengthened or weakened social ties. In this paper, we focus on a dynamic non-stationary social network and design a randomized algorithm, RSB, based on multi-armed bandit optimization, to maximize influence propagation over time. The algorithm produces a sequence of online decisions and calibrates its explore-exploit strategy utilizing outcomes of previous decisions. It is rigorously proven to achieve an upper-bounded regret in reward and applicable to large-scale social networks. Practical effectiveness of the algorithm is evaluated using both synthetic and real-world datasets, which demonstrates that our algorithm outperforms previous stationary methods under non-stationary conditions.
We study the problem of a seller dynamically pricing $d$ distinct types of indivisible goods, when faced with the online arrival of unit-demand buyers drawn independently from an unknown distribution. The goods are not in limited supply, but can only be produced at a limited rate and are costly to produce. The seller observes only the bundle of goods purchased at each day, but nothing else about the buyers valuation function. Our main result is a dynamic pricing algorithm for optimizing welfare (including the sellers cost of production) that runs in time and a number of rounds that are polynomial in $d$ and the approximation parameter. We are able to do this despite the fact that (i) the price-response function is not continuous, and even its fractional relaxation is a non-concave function of the prices, and (ii) the welfare is not observable to the seller. We derive this result as an application of a general technique for optimizing welfare over emph{divisible} goods, which is of independent interest. When buyers have strongly concave, Holder continuous valuation functions over $d$ divisible goods, we give a general polynomial time dynamic pricing technique. We are able to apply this technique to the setting of unit demand buyers despite the fact that in that setting the goods are not divisible, and the natural fractional relaxation of a unit demand valuation is not strongly concave. In order to apply our general technique, we introduce a novel price randomization procedure which has the effect of implicitly inducing buyers to regularize their valuations with a strongly concave function. Finally, we also extend our results to a limited-supply setting in which the number of copies of each good cannot be replenished.
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