This paper studies a new variant of the stochastic multi-armed bandits problem where auxiliary information about the arm rewards is available in the form of control variates. In many applications like queuing and wireless networks, the arm rewards are functions of some exogenous variables. The mean values of these variables are known a priori from historical data and can be used as control variates. Leveraging the theory of control variates, we obtain mean estimates with smaller variance and tighter confidence bounds. We develop an upper confidence bound based algorithm named UCB-CV and characterize the regret bounds in terms of the correlation between rewards and control variates when they follow a multivariate normal distribution. We also extend UCB-CV to other distributions using resampling methods like Jackknifing and Splitting. Experiments on synthetic problem instances validate performance guarantees of the proposed algorithms.

The combinatorial stochastic semi-bandit problem is an extension of the classical multi-armed bandit problem in which an algorithm pulls more than one arm at each stage and the rewards of all pulled arms are revealed. One difference with the single arm variant is that the dependency structure of the arms is crucial. Previous works on this setting either used a worst-case approach or imposed independence of the arms. We introduce a way to quantify the dependency structure of the problem and design an algorithm that adapts to it. The algorithm is based on linear regression and the analysis develops techniques from the linear bandit literature. By comparing its performance to a new lower bound, we prove that it is optimal, up to a poly-logarithmic factor in the number of pulled arms.

When working with real-world insurance data, practitioners often encounter challenges during the data preparation stage that can undermine the statistical validity and reliability of downstream modeling. This study illustrates that conventional data preparation procedures such as random train-test partitioning, often yield unreliable and unstable results when confronted with highly imbalanced insurance loss data. To mitigate these limitations, we propose a novel data preparation framework leveraging two recent statistical advancements: support points for representative data splitting to ensure distributional consistency across partitions, and the Chatterjee correlation coefficient for initial, non-parametric feature screening to capture feature relevance and dependence structure. We further integrate these theoretical advances into a unified, efficient framework that also incorporates missing-data handling, and embed this framework within our custom InsurAutoML pipeline. The performance of the proposed approach is evaluated using both simulated datasets and datasets often cited in the academic literature. Our findings definitively demonstrate that incorporating statistically rigorous data preparation methods not only significantly enhances model robustness and interpretability but also substantially reduces computational resource requirements across diverse insurance loss modeling tasks. This work provides a crucial methodological upgrade for achieving reliable results in high stakes insurance applications.

A.1.1 V ariance Preserving SDE as a potential function We can re-express the widely used V ariance Preserving (VP-SDE) (DDPM): dY