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1. Fair Online Influence Maximization

   Wang, Xiangqi; Zhang, Shaokun; Aguilar_Escamilla, Jose E; Wu, Qingyun; Zhang, Xiangliang; Kang, Jian; Wang, Huazheng (June 2025, Transactions on machine learning research)

   Fair influence maximization in networks has been actively studied to ensure equity in fields like viral marketing and public health. Existing studies often assume an offline setting, meaning that the learner identifies a set of seed nodes with known per-edge activation probabilities. In this paper, we study the problem of fair online influence maximization, i.e., without knowing the ground-truth activation probabilities. The learner in this problem aims to maximally propagate the information among demographic groups, while interactively selecting seed nodes and observing the activation feedback on the fly. We propose Fair Online Influence Maximization (FOIM) framework that can solve the online influence maximization problem under a wide range of fairness notions. Given a fairness notion, FOIM solves the problem with a combinatorial multi-armed bandit algorithm for balancing exploration-exploitation and an offline fair influence maximization oracle for seed nodes selection. FOIM enjoys sublinear regret when the fairness notion satisfies two mild conditions, i.e., monotonicity and bounded smoothness. Our analyses show that common fairness notions, including maximin fairness, diversity fairness, and welfare function, all satisfy the condition, and we prove the corresponding regret upper bounds under these notions. Extensive empirical evaluations on three real-world networks demonstrate the efficacy of our proposed framework. 

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2. Fairness of Exposure in Stochastic Bandits

   Wang, Lequn; Bai, Yiwei; Sun, Wen; Joachims, Thorsten (January 2021, International Conference on Machine Learning)

   Contextual bandit algorithms have become widely used for recommendation in online systems (e.g. marketplaces, music streaming, news), where they now wield substantial influence on which items get shown to users. This raises questions of fairness to the items — and to the sellers, artists, and writers that benefit from this exposure. We argue that the conventional bandit formulation can lead to an undesirable and unfair winner-takes-all allocation of exposure. To remedy this problem, we propose a new bandit objective that guarantees merit-based fairness of exposure to the items while optimizing utility to the users. We formulate fairness regret and reward regret in this setting and present algorithms for both stochastic multi-armed bandits and stochastic linear bandits. We prove that the algorithms achieve sublinear fairness regret and reward regret. Beyond the theoretical analysis, we also provide empirical evidence that these algorithms can allocate exposure to different arms effectively. 

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3. Online Learning with an Unknown Fairness Metric

   Gillen, S; Jung, C; Kearns, M; Roth, A (January 2019, Neural information Processing Systems (NeurIPS))

   We consider the problem of online learning in the linear contextual bandits setting, but in which there are also strong individual fairness constraints governed by an unknown similarity metric. These constraints demand that we select similar actions or individuals with approximately equal probability, which may be at odds with optimizing reward, thus modeling settings where profit and social policy are in tension. We assume we learn about an unknown Mahalanobis similarity metric from only weak feedback that identifies fairness violations, but does not quantify their extent. This is intended to represent the interventions of a regulator who “knows unfairness when he sees it” but nevertheless cannot enunciate a quantitative fairness metric over individuals. Our main result is an algorithm in the adversarial context setting that has a number of fairness violations that depends only logarithmically on T, while obtaining an optimal O(√T) regret bound to the best fair policy. 

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4. Offline Contextual Bandits with High Probability Fairness Guarantees

   Metevier, Blossom; Giguere, Stephen; Brockman, Sarah; Kobren, Ari; Brun, Yuriy; Brunskill, Emma; Thomas, Philip (December 2019, Advances in neural information processing systems)

   We present RobinHood, an offline contextual bandit algorithm designed to satisfy a broad family of fairness constraints. Our algorithm accepts multiple fairness definitions and allows users to construct their own unique fairness definitions for the problem at hand. We provide a theoretical analysis of RobinHood, which includes a proof that it will not return an unfair solution with probability greater than a user-specified threshold. We validate our algorithm on three applications: a tutoring system in which we conduct a user study and consider multiple unique fairness definitions; a loan approval setting (using the Statlog German credit data set) in which well-known fairness definitions are applied; and criminal recidivism (using data released by ProPublica). In each setting, our algorithm is able to produce fair policies that achieve performance competitive with other offline and online contextual bandit algorithms. 

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5. Instance-optimal PAC Algorithms for Contextual Bandits

   Li, Zhaoqi; Ratliff, Lillian; Nassif, Houssam; Jamieson, Kevin; Jain, Lalit (January 2022, Advances in neural information processing systems)

   Koyejo, S.; Mohamed, S.; Agarwal, A.; Belgrave, D.; Cho, K.; Oh, A. (Ed.)

   In the stochastic contextual bandit setting, regret-minimizing algorithms have been extensively researched, but their instance-minimizing best-arm identification counterparts remain seldom studied. In this work, we focus on the stochastic bandit problem in the (ǫ, δ)-PAC setting: given a policy class Π the goal of the learner is to return a policy π ∈ Π whose expected reward is within ǫ of the optimal policy with probability greater than 1 − δ. We characterize the first instance-dependent PAC sample complexity of contextual bandits through a quantity ρΠ, and provide matching upper and lower bounds in terms of ρΠ for the agnostic and linear contextual best-arm identification settings. We show that no algorithm can be simultaneously minimax-optimal for regret minimization and instance-dependent PAC for best-arm identification. Our main result is a new instance-optimal and computationally efficient algorithm that relies on a polynomial number of calls to an argmax oracle. 

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