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Can Adaptive Gradient Methods Converge under Heavy-Tailed Noise? A Case Study of AdaGrad Shallow ReLU$^s$ Networks in $L^p$-Type and Sobolev Spaces: Approximation and Path-Norm Controlled Generalization On Stability and Decomposition of Sample Quantiles under Heavy-Tailed Distributions Improved Baselines with Representation Autoencoders Symmetry-Compatible Principle for Optimizer Design: Embeddings, LM Heads, SwiGLU MLPs, and MoE Routers Feature Learning in Linear-Width Two-Layer Networks: Two vs. One Step of Gradient Descent A Two-Parameter Weibull Framework for Diagnosing Transformer Weight Distributions Calibeating for general proper losses: A Bregman divergence approach Dimension-Free Convergence of Discrete Diffusion Models: Adjoint Equations Induce the Right Space Sample-efficient inductive matrix completion with noise and inexact side-information Multi-task Linear Regression without Eigenvalue Lower Bounds: Adaptivity, Robustness, and Safety XAI and Statistical Analysis for Reliable Intrusion Detection in the UAVIDS-2025 Dataset: From Tree to Hybrid and Tabular DNN Ensembles Reasoning Models Don't Just Think Longer, They Move Differently TabPFN-3: Technical Report Reframing preprocessing selection as model-internal calibration in near-infrared spectroscopy: A large-scale benchmark of operator-adaptive PLS and Ridge models Towards a holistic understanding of Selection Bias for Causal Effect Identification Adaptive Kernel Density Estimation with Pre-training Coreset-Induced Conditional Velocity Flow Matching RISED: A Pre-Deployment Evaluation Framework for High-Stakes AI Decision-Support Systems, with Application to Healthcare ISOMORPH: A Supply Chain Digital Twin for Simulation, Dataset Generation, and Forecasting Benchmarks Yield Curves Dynamics Using Variational Autoencoders Under No-arbitrage Model-based Bootstrap of Controlled Markov Chains Online Learning-to-Defer with Varying Experts Self-Supervised Laplace Approximation for Bayesian Uncertainty Quantification Keeping Score: Efficiency Improvements in Neural Likelihood Surrogate Training via Score-Augmented Loss Functions One-Step Generative Modeling via Wasserstein Gradient Flows Exact Stiefel Optimization for Probabilistic PLS: Closed-Form Updates, Error Bounds, and Calibrated Uncertainty A Composite Activation Function for Learning Stable Binary Representations Adaptive Calibration in Non-Stationary Environments Real vs. Semi-Simulated: Rethinking Evaluation for Treatment Effect Estimation Federated Language Models Under Bandwidth Budgets: Distillation Rates and Conformal Coverage On Variance Reduction in Learning Mean Flows When Attention Beats Fourier: Multi-Scale Transformers for PDE Solving on Irregular Domains A Refined Generalization Analysis for Extreme Multi-class Supervised Contrastive Representation Learning Ensemble Distributionally Robust Bayesian Optimisation The Proxy Presumption: From Semantic Embeddings to Valid Social Measures Modulated learning for private and distributed regression with just a single sample per client device Query-efficient model evaluation using cached responses Order-Agnostic Autoregressive Modelling with Missing Data Grokking or Glitching? 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Complete version Beyond Fixed False Discovery Rates: Post-Hoc Conformal Selection with E-Variables Beyond Augmented-Action Surrogates for Multi-Expert Learning-to-Defer Spatio-temporal probabilistic forecast using MMAF-guided learning Conformal Policy Control The Implicit Curriculum: Learning Dynamics in RL with Verifiable Rewards Probabilistic NDVI Forecasting from Sparse Satellite Time Series and Weather Covariates Constrained Policy Optimization with Cantelli-Bounded Value-at-Risk Factorizable joint shift revisited Feature Learning Dynamics in Infinite-Depth Neural Networks Statistically-Guided Meta-Learning for Cross-Deployment Activity Recognition in Distributed Fiber-Optic Sensing DAPS++: Rethinking Diffusion Inverse Problems with Decoupled Posterior Annealing Branching Flows: Discrete, Continuous, and Manifold Flow Matching with Splits and Deletions Neural ARFIMA model for forecasting BRIC exchange rates with long memory Neural Stochastic Differential Equations on Compact State Spaces: Theory, Methods, and Application to Suicide Risk Modeling BOOST: A Data-Driven Framework for the Automated Joint Selection of Kernel and Acquisition Functions in Bayesian Optimization Random Walk Learning and the Pac-Man Attack Random Matrix Theory for Deep Learning: Beyond Eigenvalues of Linear Models Post-Training Augmentation Invariance Optimizing LLM Inference: Fluid-Guided Online Scheduling with Memory Constraints Dataset-Driven Channel Masks in Transformers for Multivariate Time Series
Variational Proximal Policy Optimization
Ousmane Amadou Dia · 2026-06-06 · via stat updates on arXiv.org

Reinforcement Learning from Human Feedback via Proximal Policy Optimization often suffers from policy mode collapse, brittle exploration loops, and distribution drift. This paper introduces Variational Proximal Policy Optimization (\(\textsc{VP}_2\textsc{O}\)), a particle-based variational inference framework that maps policy optimization to Stein Variational Gradient Descent within a Mixture-of-Experts architecture. By leveraging functional kernels over localized expert prototypes alongside an expert orthogonalization loss, \(\textsc{VP}_2\textsc{O}\) introduces a geometry-based proximal-control mechanism that can reduce reliance on fixed clipping or KL schedules. Our results on a 33B/4B sparse Mixture-of-Experts model show several improvements across complex reasoning benchmarks, establishing a \(+\mathbf{179}\) ELO gain on Codeforces and a \(\mathbf{32\%}\) reduction in token count on AIME mathematical reasoning tasks.