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Approximate Leave-One-Out Cross-Validation (ALO-CV) is a method that has been proposed to estimate the generalization error of a regularized estimator in the high-dimensional regime where dimension and sample size are of the same order, the…

Statistics Theory · Mathematics 2026-02-13 Pierre C Bellec

This paper presents AGGLIO (Accelerated Graduated Generalized LInear-model Optimization), a stage-wise, graduated optimization technique that offers global convergence guarantees for non-convex optimization problems whose objectives offer…

Optimization and Control · Mathematics 2021-11-09 Debojyoti Dey , Bhaskar Mukhoty , Purushottam Kar

Due to the privacy protection or the difficulty of data collection, we cannot observe individual outputs for each instance, but we can observe aggregated outputs that are summed over multiple instances in a set in some real-world…

Machine Learning · Statistics 2022-10-05 Tomoharu Iwata

Cross-validation is one of the most widely used methods for model selection and evaluation; its efficiency for large covariance matrix estimation appears robust in practice, but little is known about the theoretical behavior of its error.…

Statistical Finance · Quantitative Finance 2025-09-18 Lamia Lamrani , Benoît Collins , Jean-Philippe Bouchaud

Group Relative Policy Optimization (GRPO) was introduced and used recently for promoting reasoning in LLMs under verifiable (binary) rewards. We show that the mean + variance calibration of these rewards induces a weighted contrastive loss…

Machine Learning · Computer Science 2025-10-22 Youssef Mroueh

Reinforcement learning has become a powerful paradigm for post-training large language model agents, yet credit assignment in multi-turn environments remains a challenge. Agents often receive sparse, trajectory-level rewards only at the end…

Computation and Language · Computer Science 2026-05-14 Siyuan Zhu , Chao Yu , Rongxin Yang , Zongkai Liu , Jinjun Hu , Qiwen Chen , Yibo Zhang

Constrained reinforcement learning has achieved promising progress in safety-critical fields where both rewards and constraints are considered. However, constrained reinforcement learning methods face challenges in striking the right…

Machine Learning · Computer Science 2024-10-29 Jianmina Ma , Jingtian Ji , Yue Gao

Graph aggregation is the process of computing a single output graph that constitutes a good compromise between several input graphs, each provided by a different source. One needs to perform graph aggregation in a wide variety of…

Artificial Intelligence · Computer Science 2018-06-13 Ulle Endriss , Umberto Grandi

Risk estimation is at the core of many learning systems. The importance of this problem has motivated researchers to propose different schemes, such as cross validation, generalized cross validation, and Bootstrap. The theoretical…

Statistics Theory · Mathematics 2021-01-19 Ji Xu , Arian Maleki , Kamiar Rahnama Rad , Daniel Hsu

Many decision problems cannot be solved exactly and use several estimation algorithms that assign scores to the different available options. The estimation errors can have various correlations, from low (e.g. between two very different…

Machine Learning · Computer Science 2023-09-06 Theo Delemazure , François Durand , Fabien Mathieu

Offline preference optimization allows fine-tuning large models directly from offline data, and has proved effective in recent alignment practices. We propose generalized preference optimization (GPO), a family of offline losses…

Group Relative Policy Optimization (GRPO) is widely used for reinforcement learning with verifiable rewards, but it often suffers from advantage collapse: when all rollouts in a group receive the same reward, the group yields zero relative…

Machine Learning · Computer Science 2026-04-02 Yu Xia , Canwen Xu , Zhewei Yao , Julian McAuley , Yuxiong He

AUC (area under ROC curve) is an important evaluation criterion, which has been popularly used in many learning tasks such as class-imbalance learning, cost-sensitive learning, learning to rank, etc. Many learning approaches try to optimize…

Machine Learning · Computer Science 2020-07-07 Wei Gao , Zhi-Hua Zhou

$L_1$ regularized logistic regression has now become a workhorse of data mining and bioinformatics: it is widely used for many classification problems, particularly ones with many features. However, $L_1$ regularization typically selects…

Machine Learning · Statistics 2015-02-12 Zhe Liu

Group-based reinforcement learning methods, like Group Relative Policy Optimization (GRPO), are widely used nowadays to post-train large language models. Despite their empirical success, they exhibit structural mismatches between reward…

Machine Learning · Computer Science 2026-01-09 Aleksandar Fontana , Marco Simoni , Giulio Rossolini , Andrea Saracino , Paolo Mori

The paper considers the problem of out-of-sample risk estimation under the high dimensional settings where standard techniques such as $K$-fold cross validation suffer from large biases. Motivated by the low bias of the leave-one-out cross…

Methodology · Statistics 2020-02-12 Kamiar Rahnama Rad , Arian Maleki

Group Relative Policy Optimization (GRPO) has recently emerged as a practical recipe for aligning large language models with verifiable objectives. However, under sparse terminal rewards, GRPO often stalls because rollouts within a group…

Machine Learning · Computer Science 2026-02-04 Baohao Liao , Hanze Dong , Xinxing Xu , Christof Monz , Jiang Bian

Diffusion large language models (dLLMs), which offer a promising alternative to traditional autoregressive LLMs, have recently shown strong results in pretraining. However, due to their lack of tractable sequence-level likelihoods, they…

Machine Learning · Computer Science 2026-02-03 Anthony Zhan

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a promising paradigm for post-training reasoning models. However, group-based methods such as Group Relative Policy Optimization (GRPO) face a critical dilemma in…

Machine Learning · Computer Science 2026-04-07 Yuning Wu , Ke Wang , Devin Chen , Kai Wei

We introduce an alternative to the notion of `fast rate' in Learning Theory, which coincides with the optimal error rate when the given class happens to be convex and regular in some sense. While it is well known that such a rate cannot…

Statistics Theory · Mathematics 2015-02-26 Shahar Mendelson