Large language models (LLMs) are being used in data science code generation tasks, but they often struggle with complex sequential tasks, leading to logical errors. Their application to geospatial data processing is particularly challenging due to difficulties in incorporating complex data structures and spatial constraints, effectively utilizing diverse function calls, and the tendency to hallucinate less-used geospatial libraries. To tackle these problems, we introduce GeoAgent, a new interactive framework designed to help LLMs handle geospatial data processing more effectively. GeoAgent pioneers the integration of a code interpreter, static analysis, and Retrieval-Augmented Generation (RAG) techniques within a Monte Carlo Tree Search (MCTS) algorithm, offering a novel approach to geospatial data processing. In addition, we contribute a new benchmark specifically designed to evaluate the LLM-based approach in geospatial tasks. This benchmark leverages a variety of Python libraries and includes both single-turn and multi-turn tasks such as data acquisition, data analysis, and visualization. By offering a comprehensive evaluation among diverse geospatial contexts, this benchmark sets a new standard for developing LLM-based approaches in geospatial data analysis tasks. Our findings suggest that relying solely on knowledge of LLM is insufficient for accurate geospatial task programming, which requires coherent multi-step processes and multiple function calls. Compared to the baseline LLMs, the proposed GeoAgent has demonstrated superior performance, yielding notable improvements in function calls and task completion. In addition, these results offer valuable insights for the future development of LLM agents in automatic geospatial data analysis task programming.

Distributed optimization and learning has recently garnered great attention due to its wide applications in sensor networks, smart grids, machine learning, and so forth. Despite rapid development, existing distributed optimization and learning algorithms require each agent to exchange messages with its neighbors, which may expose sensitive information and raise significant privacy concerns. In this survey paper, we overview privacy-preserving distributed optimization and learning methods. We first discuss cryptography, differential privacy, and other techniques that can be used for privacy preservation and indicate their pros and cons for privacy protection in distributed optimization and learning. We believe that among these approaches, differential privacy is most promising due to its low computational and communication complexities, which are extremely appealing for modern learning based applications with high dimensions of optimization variables. We then introduce several differential-privacy algorithms that can simultaneously ensure privacy and optimization accuracy. Moreover, we provide example applications in several machine learning problems to confirm the real-world effectiveness of these algorithms. Finally, we highlight some challenges in this research domain and discuss future directions.

In this paper, we study the MNL-Bandit problem in a non-stationary environment and present an algorithm with a worst-case expected regret of $\tilde{O}\left( \min \left\{ \sqrt{NTL}\;,\; N^{\frac{1}{3}}(\Delta_{\infty}^{K})^{\frac{1}{3}} T^{\frac{2}{3}} + \sqrt{NT}\right\}\right)$. Here $N$ is the number of arms, $L$ is the number of changes and $\Delta_{\infty}^{K}$ is a variation measure of the unknown parameters. Furthermore, we show matching lower bounds on the expected regret (up to logarithmic factors), implying that our algorithm is optimal. Our approach builds upon the epoch-based algorithm for stationary MNL-Bandit in Agrawal et al. 2016. However, non-stationarity poses several challenges and we introduce new techniques and ideas to address these. In particular, we give a tight characterization for the bias introduced in the estimators due to non stationarity and derive new concentration bounds.

Data-driven sequential decision has found a wide range of applications in modern operations management, such as dynamic pricing, inventory control, and assortment optimization. Most existing research on data-driven sequential decision focuses on designing an online policy to maximize the revenue. However, the research on uncertainty quantification on the underlying true model function (e.g., demand function), a critical problem for practitioners, has not been well explored. In this paper, using the problem of demand function prediction in dynamic pricing as the motivating example, we study the problem of constructing accurate confidence intervals for the demand function. The main challenge is that sequentially collected data leads to significant distributional bias in the maximum likelihood estimator or the empirical risk minimization estimate, making classical statistics approaches such as the Wald's test no longer valid. We address this challenge by developing a debiased approach and provide the asymptotic normality guarantee of the debiased estimator. Based this the debiased estimator, we provide both point-wise and uniform confidence intervals of the demand function.