Contaminated Multi-task Learning with Heterogeneity: Fundamental Limits and Optimal Algorithms

Integrating information across related tasks can improve estimation and prediction in transfer, multi-task, and federated learning, but contamination and heterogeneity make robust borrowing challenging. We study a contaminated multi-task empirical risk minimization (ERM) framework in which an $ε$ fraction of $K$ tasks, each with sample size $n$, may be arbitrarily contaminated while the remaining tasks are heterogeneous. Our goal is to estimate both the global minimizer of the average risk and the clean task-specific minimizers, thereby combining robustness and personalization. In the Gaussian mean model, we show that several common paradigms, including adaptive and robust regularization around a shared center, global matrix regularization, decomposition-based regularization, and score-based outlier-task detection, all suffer from a worst-case contamination error of order $ε\sqrt{d/n}$, which is suboptimal compared to the lower bound $ε/\sqrt{n}$. This identifies a dimension-dependent barrier for these approaches. We then establish minimax lower bounds for a general heterogeneous ERM setting and propose a computationally efficient filtering-based robust multi-task gradient descent method. Under local strong convexity, smoothness, and sub-Gaussian gradient assumptions, the proposed method attains high-probability upper bounds matching the minimax rates up to logarithmic factors over a broad regime. In particular, it removes the extra $\sqrt{d}$ contamination dependence of many regularization-based methods and score-based outlier detection, while achieving personalization to local tasks under strong heterogeneity. Simulations and a real-data analysis demonstrate strong robustness and personalization relative to a broad range of benchmark methods.

Segmenting Human-LLM Co-authored Text via Change Point Detection

The rise of large language models (LLMs) has created an urgent need to distinguish between human-written and LLM-generated text to ensure authenticity and societal trust. Existing detectors typically provide a binary classification for an entire passage; however, this is insufficient for human--LLM co-authored text, where the objective is to localize specific segments authored by humans or LLMs. To bridge this gap, we propose algorithms to segment text into human- and LLM-authored pieces. Our key observation is that such a segmentation task is conceptually similar to classical change point detection in time-series analysis. Leveraging this analogy, we adapt change point detection to LLM-generated text detection, develop a weighted algorithm and a generalized algorithm to accommodate heterogeneous detection score variability, and establish the minimax optimality of our procedure. Empirically, we demonstrate the strong performance of our approach against a wide range of existing baselines.

Federated Transfer Learning with Differential Privacy

Federated learning is gaining increasing popularity, with data heterogeneity and privacy being two prominent challenges. In this paper, we address both issues within a federated transfer learning framework, aiming to enhance learning on a target data set by leveraging information from multiple heterogeneous source data sets while adhering to privacy constraints. We rigorously formulate the notion of \textit{federated differential privacy}, which offers privacy guarantees for each data set without assuming a trusted central server. Under this privacy constraint, we study three classical statistical problems, namely univariate mean estimation, low-dimensional linear regression, and high-dimensional linear regression. By investigating the minimax rates and identifying the costs of privacy for these problems, we show that federated differential privacy is an intermediate privacy model between the well-established local and central models of differential privacy. Our analyses incorporate data heterogeneity and privacy, highlighting the fundamental costs of both in federated learning and underscoring the benefit of knowledge transfer across data sets.