Social relations have been widely incorporated into recommender systems to alleviate data sparsity problem. However, raw social relations don't always benefit recommendation due to their inferior quality and insufficient quantity, especially for inactive users, whose interacted items are limited. In this paper, we propose a novel social recommendation method called LSIR (\textbf{L}earning \textbf{S}ocial Graph for \textbf{I}nactive User \textbf{R}ecommendation) that learns an optimal social graph structure for social recommendation, especially for inactive users. LSIR recursively aggregates user and item embeddings to collaboratively encode item and user features. Then, graph structure learning (GSL) is employed to refine the raw user-user social graph, by removing noisy edges and adding new edges based on the enhanced embeddings. Meanwhile, mimic learning is implemented to guide active users in mimicking inactive users during model training, which improves the construction of new edges for inactive users. Extensive experiments on real-world datasets demonstrate that LSIR achieves significant improvements of up to 129.58\% on NDCG in inactive user recommendation. Our code is available at~\url{https://github.com/liun-online/LSIR}.

Physical inactivity remains a major public health concern, having associations with adverse health outcomes such as cardiovascular disease and type-2 diabetes. Mobile health applications present a promising avenue for low-cost, scalable physical activity promotion, yet often suffer from small effect sizes and low adherence rates, particularly in comparison to human coaching. Goal-setting is a critical component of health coaching that has been underutilized in adaptive algorithms for mobile health interventions. This paper introduces a modification to the Thompson sampling algorithm that places emphasis on individualized goal-setting by optimizing personalized reward functions. As a step towards supporting goal-setting, this paper offers a balanced approach that can leverage shared structure while optimizing individual preferences and goals. We prove that our modification incurs only a constant penalty on the cumulative regret while preserving the sample complexity benefits of data sharing. In a physical activity simulator, we demonstrate that our algorithm achieves substantial improvements in cumulative regret compared to baselines that do not share data or do not optimize for individualized rewards.

Recently, there has been an increasing adoption of differential privacy guided algorithms for privacy-preserving machine learning tasks. However, the use of such algorithms comes with trade-offs in terms of algorithmic fairness, which has been widely acknowledged. Specifically, we have empirically observed that the classical collaborative filtering method, trained by differentially private stochastic gradient descent (DP-SGD), results in a disparate impact on user groups with respect to different user engagement levels. This, in turn, causes the original unfair model to become even more biased against inactive users. To address the above issues, we propose \textbf{DP-Fair}, a two-stage framework for collaborative filtering based algorithms. Specifically, it combines differential privacy mechanisms with fairness constraints to protect user privacy while ensuring fair recommendations. The experimental results, based on Amazon datasets, and user history logs collected from Etsy, one of the largest e-commerce platforms, demonstrate that our proposed method exhibits superior performance in terms of both overall accuracy and user group fairness on both shallow and deep recommendation models compared to vanilla DP-SGD.