Shang Liu

Shang Liu, Jiashuo Jiang, Xiaocheng Li

In this paper, we study the problem of bandits with knapsacks (BwK) in a non-stationary environment. The BwK problem generalizes the multi-arm bandit (MAB) problem to model the resource consumption associated with playing each arm. At each time, the decision maker/player chooses to play an arm, and s/he will receive a reward and consume certain amount of resource from each of the multiple resource types. The objective is to maximize the cumulative reward over a finite horizon subject to some knapsack constraints on the resources. Existing works study the BwK problem under either a stochastic or adversarial environment. Our paper considers a non-stationary environment which continuously interpolates between these two extremes. We first show that the traditional notion of variation budget is insufficient to characterize the non-stationarity of the BwK problem for a sublinear regret due to the presence of the constraints, and then we propose a new notion of global non-stationarity measure. We employ both non-stationarity measures to derive upper and lower bounds for the problem. Our results are based on a primal-dual analysis of the underlying linear programs and highlight the interplay between the constraints and the non-stationarity. Finally, we also extend the non-stationarity measure to the problem of online convex optimization with constraints and obtain new regret bounds accordingly.

Zixin Rao, Youssef Mohamed, Shang Liu et al.

Large Language Models (LLMs), such as GPT-4 and Llama, have demonstrated remarkable abilities in generating natural language. However, they also pose security and integrity challenges. Existing countermeasures primarily focus on distinguishing AI-generated content from human-written text, with most solutions tailored for English. Meanwhile, authorship attribution--determining which specific LLM produced a given text--has received comparatively little attention despite its importance in forensic analysis. In this paper, we present DA-MTL, a multi-task learning framework that simultaneously addresses both text detection and authorship attribution. We evaluate DA-MTL on nine datasets and four backbone models, demonstrating its strong performance across multiple languages and LLM sources. Our framework captures each task's unique characteristics and shares insights between them, which boosts performance in both tasks. Additionally, we conduct a thorough analysis of cross-modal and cross-lingual patterns and assess the framework's robustness against adversarial obfuscation techniques. Our findings offer valuable insights into LLM behavior and the generalization of both detection and authorship attribution.

Shang Liu, Zhongze Cai, Xiaocheng Li

In this paper, we consider the uncertainty quantification problem for regression models. Specifically, we consider an individual calibration objective for characterizing the quantiles of the prediction model. While such an objective is well-motivated from downstream tasks such as newsvendor cost, the existing methods have been largely heuristic and lack of statistical guarantee in terms of individual calibration. We show via simple examples that the existing methods focusing on population-level calibration guarantees such as average calibration or sharpness can lead to harmful and unexpected results. We propose simple nonparametric calibration methods that are agnostic of the underlying prediction model and enjoy both computational efficiency and statistical consistency. Our approach enables a better understanding of the possibility of individual calibration, and we establish matching upper and lower bounds for the calibration error of our proposed methods. Technically, our analysis combines the nonparametric analysis with a covering number argument for parametric analysis, which advances the existing theoretical analyses in the literature of nonparametric density estimation and quantile bandit problems. Importantly, the nonparametric perspective sheds new theoretical insights into regression calibration in terms of the curse of dimensionality and reconciles the existing results on the impossibility of individual calibration. To our knowledge, we make the first effort to reach both individual calibration and finite-sample guarantee with minimal assumptions in terms of conformal prediction. Numerical experiments show the advantage of such a simple approach under various metrics, and also under covariates shift. We hope our work provides a simple benchmark and a starting point of theoretical ground for future research on regression calibration.