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Reinforcement learning (RL) has proven remarkably effective at improving the accuracy of language models in verifiable and deterministic domains like mathematics. Here, we examine if current RL methods are also effective at optimizing…

Critic-free reinforcement learning methods, particularly group policies, have attracted considerable attention for their efficiency in complex tasks. However, these methods rely heavily on multiple sampling and comparisons within the policy…

We introduce Parametric Density Path Optimization (PDPO), a novel method for computing action-minimizing paths between probability densities. The core idea is to represent the target probability path as the pushforward of a reference…

Structural estimation is an important methodology in empirical economics, and a large class of structural models are estimated through the generalized method of moments (GMM). Traditionally, selection of structural models has been performed…

We analyze the statistical properties of generalized cross-validation (GCV) and leave-one-out cross-validation (LOOCV) applied to early-stopped gradient descent (GD) in high-dimensional least squares regression. We prove that GCV is…

The aim of this paper is to provide several novel upper bounds on the excess risk with a primal focus on classification problems. We suggest two approaches and the obtained bounds are represented via the distribution dependent local…

Recent advances in large reasoning models have leveraged reinforcement learning with verifiable rewards (RLVR) to improve reasoning capabilities. However, scaling these methods typically requires extensive rollout computation and large…

The high cost and data scarcity in scientific exploration have motivated the use of large language models (LLMs) as knowledge-driven components in Bayesian optimization (BO). However, existing approaches typically embed LLMs directly into…

Penalized logistic regression methods are frequently used to investigate the relationship between a binary outcome and a set of explanatory variables. The model performance can be assessed by measures such as the concordance statistic…

Reinforcement learning with verifiable rewards (RLVR), due to the deterministic verification, becomes a dominant paradigm for enhancing the reasoning ability of large language models (LLMs). The community witnesses the rapid change from the…

Current large language model post-training optimizes a risk-neutral objective that maximizes expected reward, yet evaluation relies heavily on risk-seeking metrics like Pass@k (at least one success in k trials) and Max@k (maximum reward…

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a promising approach to improve the reasoning abilities of Large Language Models (LLMs). Among RLVR algorithms, Group Relative Policy Optimization (GRPO) and its variants…

The problem of constrained reinforcement learning (CRL) holds significant importance as it provides a framework for addressing critical safety satisfaction concerns in the field of reinforcement learning (RL). However, with the introduction…

Reinforcement learning with verifiable reward has recently emerged as a central paradigm for post-training large language models (LLMs); however, prevailing mean-based methods, such as Group Relative Policy Optimization (GRPO), suffer from…

The masking-one-out (MOO) procedure, masking an observed entry and comparing it versus its imputed values, is a very common procedure for comparing imputation models. We study the optimum of this procedure and generalize it to a missing…

Many varieties of cross validation would be statistically appealing for the estimation of smoothing and other penalized regression hyperparameters, were it not for the high cost of evaluating such criteria. Here it is shown how to…

Ensemble disagreement is widely used as a proxy for epistemic uncertainty in medical image segmentation. In practice, many studies form ensembles via K-fold cross-validation (CV), yet refer to them as ``deep ensembles'' (DE). Because CV…

How to efficiently identify multiple-input multiple-output (MIMO) linear parameter-varying (LPV) discrete-time state-space (SS) models with affine dependence on the scheduling variable still remains an open question, as identification…

Improving and understanding the training dynamics and reasoning of Large Language Models (LLMs) has become essential for their deployment in AI-based security tools, such as software vulnerability detection. In this work, we present an…

Recent advances in large language models (LLMs) have shown strong reasoning capabilities through large-scale pretraining and post-training reinforcement learning, demonstrated by DeepSeek-R1. However, current post-training methods, such as…