Motivated by value function estimation in reinforcement learning, we study statistical linear inverse problems, i.e., problems where the coefficients of a linear system to be solved are observed in noise. We consider penalized estimators, where performance is evaluated using a matrix-weighted two-norm of the defect of the estimator measured with respect to the true, unknown coefficients. Two objective functions are considered depending whether the error of the defect measured with respect to the noisy coefficients is squared or unsquared. We propose simple, yet novel and theoretically well-founded data-dependent choices for the regularization parameters for both cases that avoid data-splitting. A distinguishing feature of our analysis is that we derive deterministic error bounds in terms of the error of the coefficients, thus allowing the complete separation of the analysis of the stochastic properties of these errors. We show that our results lead to new insights and bounds for linear value function estimation in reinforcement learning.
Uncertainty-Penalized Reinforcement Learning from Human Feedback with Diverse Reward LoRA Ensembles
National University of Defense Technology（国防科技大学）；State Key Laboratory of Complex & Critical Software Environment（复杂与关键软件环境国家重点实验室）；Harbin Institute of Technology (Shenzhen)（哈尔滨工业大学（深圳））；Peng Cheng Laboratory（鹏城实验室）
Generalized Linear Models with Structured Sparsity Estimators
North Carolina State University（北卡罗来纳州立大学）
本文在广义线性模型中引入结构稀疏估计。Stucky和van de Geer（2018）最近针对固定设计和正态误差引入了最小二乘损失中的结构稀疏估计。我们扩展他们的结果去偏结构稀疏估计与广义线性模型为基础的损失。结构化稀疏估计是指在所选范数中使用可能的稀疏结构的惩罚损失函数。这些包括加权群套索，套索和规范产生的凸锥。最大的困难是不清楚如何证明两个预言不等式。第一个是初始惩罚广义线性模型估计。由于不清楚特定的可行加权逐点回归如何适合惩罚广义线性模型的预言不等式，我们需要第二个预言不等式来获得广义线性模型的二阶偏导数的样本估计的近似逆的预言界。我们的贡献有五个方面：1。通过证明隐含条件而不是假设隐含条件，将已有的预言不等式结果推广到惩罚广义线性模型中。其中一个关键问题是一个样本单点边界条件的证明及其在预言不等式中的应用。2.我们的研究结果甚至覆盖非次高斯误差和回归。3.我们提供了一个可行的加权nodewise回归证明，推广了文献中的结果，从一个简单的l_1范数的使用，从凸锥产生的规范。4.我们认识到，在可行的逐节点回归证明中使用的范数应该弱于或等于惩罚广义线性模型损失中的范数。5.通过求广义线性模型损失的奇异样本二阶偏导数的近似逆，可以消除第一步估计的偏差。
Penalized Empirical Likelihood for Doubly Robust Causal Inference under Contamination in High Dimensions
Department of Mathematics and Physics, Gangneung-Wonju National University（数学与物理系，江陵-Wonju国立大学）；Department of Applied Statistics, Yonsei University（应用统计学系，延世大学）；Department of Statistics, Dongguk University（统计学系，东国大学）；Department of Marketing Bigdata, Mokwon University（市场营销大数据系，摩斯大学）；Department of Data Science, Gangneung-Wonju National University（数据科学系，江陵-Wonju国立大学）
