Fast Online Learning with Gaussian Prior-Driven Hierarchical Unimodal Thompson Sampling

We study a type of Multi-Armed Bandit (MAB) problems in which arms with a Gaussian reward feedback are clustered. Such an arm setting finds applications in many real-world problems, for example, mmWave communications and portfolio management with risky assets, as a result of the universality of the Gaussian distribution. Based on the Thompson Sampling algorithm with Gaussian prior (TSG) algorithm for the selection of the optimal arm, we propose our Thompson Sampling with Clustered arms under Gaussian prior (TSCG) specific to the 2-level hierarchical structure. We prove that by utilizing the 2-level structure, we can achieve a lower regret bound than we do with ordinary TSG. In addition, when the reward is Unimodal, we can reach an even lower bound on the regret by our Unimodal Thompson Sampling algorithm with Clustered Arms under Gaussian prior (UTSCG). Each of our proposed algorithms are accompanied by theoretical evaluation of the upper regret bound, and our numerical experiments confirm the advantage of our proposed algorithms.

Beyond Static Snapshots: Dynamic Modeling and Forecasting of Group-Level Value Evolution with Large Language Models

Social simulation is critical for mining complex social dynamics and supporting data-driven decision making. LLM-based methods have emerged as powerful tools for this task by leveraging human-like social questionnaire responses to model group behaviors. Existing LLM-based approaches predominantly focus on group-level values at discrete time points, treating them as static snapshots rather than dynamic processes. However, group-level values are not fixed but shaped by long-term social changes. Modeling their dynamics is thus crucial for accurate social evolution prediction--a key challenge in both data mining and social science. This problem remains underexplored due to limited longitudinal data, group heterogeneity, and intricate historical event impacts. To bridge this gap, we propose a novel framework for group-level dynamic social simulation by integrating historical value trajectories into LLM-based human response modeling. We select China and the U.S. as representative contexts, conducting stratified simulations across four core sociodemographic dimensions (gender, age, education, income). Using the World Values Survey, we construct a multi-wave, group-level longitudinal dataset to capture historical value evolution, and then propose the first event-based prediction method for this task, unifying social events, current value states, and group attributes into a single framework. Evaluations across five LLM families show substantial gains: a maximum 30.88\% improvement on seen questions and 33.97\% on unseen questions over the Vanilla baseline. We further find notable cross-group heterogeneity: U.S. groups are more volatile than Chinese groups, and younger groups in both countries are more sensitive to external changes. These findings advance LLM-based social simulation and provide new insights for social scientists to understand and predict social value changes.