Social media have great potential for enabling public discourse on important societal issues. However, adverse effects, such as polarization and echo chambers, greatly impact the benefits of social media and call for algorithms that mitigate these effects. In this paper, we propose a novel problem formulation aimed at slightly nudging users' social feeds in order to strike a balance between relevance and diversity, thus mitigating the emergence of polarization, without lowering the quality of the feed. Our approach is based on re-weighting the relative importance of the accounts that a user follows, so as to calibrate the frequency with which the content produced by various accounts is shown to the user. We analyze the convexity properties of the problem, demonstrating the non-matrix convexity of the objective function and the convexity of the feasible set. To efficiently address the problem, we develop a scalable algorithm based on projected gradient descent. We also prove that our problem statement is a proper generalization of the undirected-case problem so that our method can also be adopted for undirected social networks. As a baseline for comparison in the undirected case, we develop a semidefinite programming approach, which provides the optimal solution. Through extensive experiments on synthetic and real-world datasets, we validate the effectiveness of our approach, which outperforms non-trivial baselines, underscoring its ability to foster healthier and more cohesive online communities.

翻译：社交媒体在促进公众讨论重要社会议题方面具有巨大潜力。然而，诸如极化和回音室等负面效应严重影响了社交媒体的益处，亟需能够缓解这些效应的算法。本文提出了一种新颖的问题框架，旨在轻微调整用户社交推送，以在相关性和多样性之间取得平衡，从而在不降低推送质量的前提下缓解极化的出现。我们的方法基于对用户所关注账户的相对重要性进行重新加权，从而校准各账户所产生内容展示给用户的频率。我们分析了该问题的凸性性质，证明了目标函数的非矩阵凸性及可行集的凸性。为了高效解决该问题，我们开发了一种基于投影梯度下降的可扩展算法。我们还证明，我们的问题表述是无向情况问题的恰当泛化，因此我们的方法也可适用于无向社交网络。作为无向情况下的比较基线，我们提出了一种半定规划方法，该方法能够提供最优解。通过在合成数据集和真实世界数据集上的广泛实验，我们验证了方法的有效性，其性能优于非平凡基线，凸显了其促进更健康、更紧密在线社区的能力。