Stochastic Approximation Methods for Distortion Risk Measure Optimization
Guanghua School of Management Peking University（北京大学光华管理学院）；School of Business and Economics Vrije Universiteit Amsterdam（荷兰阿姆斯特丹自由大学商学院）；Department of Applied Mathematics and Statistics State University of New York at Stony Brook（纽约州立大学石溪分校应用数学与统计学系）；Guanghua School of Management School of Artificial Intelligence for Science Peking University（北京大学光华管理学院人工智能科学学院）；Xiangjiang Laboratory（湘江实验室）
Distortion Risk Measures (DRMs) capture risk preferences in decision-making and serve as general criteria for managing uncertainty. This paper proposes gradient descent algorithms for DRM optimization based on two dual representations: the Distortion-Measure (DM) form and Quantile-Function (QF) form. The DM-form employs a three-timescale algorithm to track quantiles, compute their gradients, and update decision variables, utilizing the Generalized Likelihood Ratio and kernel-based density estimation. The QF-form provides a simpler two-timescale approach that avoids the need for complex quantile gradient estimation. A hybrid form integrates both approaches, applying the DM-form for robust performance around distortion function jumps and the QF-form for efficiency in smooth regions. Proofs of strong convergence and convergence rates for the proposed algorithms are provided. In particular, the DM-form achieves an optimal rate of $O(k^{-4/7})$, while the QF-form attains a faster rate of $O(k^{-2/3})$. Numerical experiments confirm their effectiveness and demonstrate substantial improvements over baselines in robust portfolio selection tasks. The method's scalability is further illustrated through integration into deep reinforcement learning. Specifically, a DRM-based Proximal Policy Optimization algorithm is developed and applied to multi-echelon dynamic inventory management, showcasing its practical applicability.
A Noise-Robust Elicit-to-Optimize Framework for Distortion Riskmetrics via Inverse Reinforcement Learning
School of Science and Engineering, The Chinese University of Hong Kong (Shenzhen)（香港中文大学（深圳）理工学院）；School of Mathematics and Statistics, Carleton University（卡尔顿大学数学与统计学院）
Supervised Learning and Large Language Model Benchmarks on Mental Health Datasets: Cognitive Distortions and Suicidal Risks in Chinese Social Media
School of Software Engineering, Beijing University of Technology（北京工业大学软件学院）；School of Nursing, Wuhan University（武汉大学护理学院）；Sorbonne Université, Institut du Cerveau – Paris Brain Institute - ICM, CNRS, Inria, Inserm, AP-HP, Hôpital de la Pitié-Salpêtrière（索邦大学、巴黎脑研究所、法国国家科学研究中心、法国国家计算机与自动化研究所、法国国家健康与医学研究院、巴黎公立医院集团、皮蒂-萨尔皮特里耶医院）
