Motivated by privacy concerns in sequential decision-making on sensitive data, we address the challenge of nonparametric contextual multi-armed bandits (MAB) under local differential privacy (LDP). We develop a uniform-confidence-bound-type estimator, showing its minimax optimality supported by a matching minimax lower bound. We further consider the case where auxiliary datasets are available, subject also to (possibly heterogeneous) LDP constraints. Under the widely-used covariate shift framework, we propose a jump-start scheme to effectively utilize the auxiliary data, the minimax optimality of which is further established by a matching lower bound. Comprehensive experiments on both synthetic and real-world datasets validate our theoretical results and underscore the effectiveness of the proposed methods.

While extensive research has explored the use of large language models (LLMs) for table-based reasoning, most approaches struggle with scalability when applied to large tables. To maintain the superior comprehension abilities of LLMs in these scenarios, we introduce ALTER(Augmentation for Large-Table-Based Reasoning)-a framework designed to harness the latent augmentation potential in both free-form natural language (NL) questions, via the query augmentor, and semi-structured tabular data, through the table augmentor. By utilizing only a small subset of relevant data from the table and supplementing it with pre-augmented schema, semantic, and literal information, ALTER achieves outstanding performance on table-based reasoning benchmarks. We also provide a detailed analysis of large-table scenarios, comparing different methods and various partitioning principles. In these scenarios, our method outperforms all other approaches and exhibits robustness and efficiency against perturbations.

We initiate the study of locally differentially private (LDP) learning with public features. We define semi-feature LDP, where some features are publicly available while the remaining ones, along with the label, require protection under local differential privacy. Under semi-feature LDP, we demonstrate that the mini-max convergence rate for non-parametric regression is significantly reduced compared to that of classical LDP. Then we propose HistOfTree, an estimator that fully leverages the information contained in both public and private features. Theoretically, HistOfTree reaches the mini-max optimal convergence rate. Empirically, HistOfTree achieves superior performance on both synthetic and real data. We also explore scenarios where users have the flexibility to select features for protection manually. In such cases, we propose an estimator and a data-driven parameter tuning strategy, leading to analogous theoretical and empirical results.

In this work, we investigate the problem of public data-assisted non-interactive LDP (Local Differential Privacy) learning with a focus on non-parametric classification. Under the posterior drift assumption, we for the first time derive the mini-max optimal convergence rate with LDP constraint. Then, we present a novel approach, the locally private classification tree, which attains the mini-max optimal convergence rate. Furthermore, we design a data-driven pruning procedure that avoids parameter tuning and produces a fast converging estimator. Comprehensive experiments conducted on synthetic and real datasets show the superior performance of our proposed method. Both our theoretical and experimental findings demonstrate the effectiveness of public data compared to private data, which leads to practical suggestions for prioritizing non-private data collection.