Variational Proximal Policy Optimization

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.