Title: Beyond Distributions: Geometric Action Control for Continuous Reinforcement Learning
Primary area: reinforcement learning
Keywords: reinforcement learning, geometric control, spherical normalization, bounded action spaces, continuous control, action generation, distribution-aware policy optimization

Abstract: Gaussian policies have dominated continuous control in deep reinforcement learning (RL), yet they suffer from a fundamental mismatch: their unbounded support requires ad-hoc squashing functions that distort the geometry of bounded action spaces.
While von Mises-Fisher (vMF) distributions offer a theoretically grounded alternative on the sphere, their reliance on Bessel functions and rejection sampling hinders practical adoption.
We propose \textbf{Geometric Action Control (GAC)}, a novel action generation paradigm that preserves the geometric benefits of spherical distributions while \textit{simplifying computation}.
GAC decomposes action generation into a direction vector and a learnable concentration parameter, enabling efficient interpolation between deterministic actions and uniform spherical noise.
This design reduces parameter count from \(2d\) to \(d+1\), and avoids the \(O(dk)\) complexity of vMF rejection sampling, achieving simple \(O(d)\) operations.
Empirically, GAC consistently matches or exceeds state-of-the-art methods across six MuJoCo benchmarks, achieving 37.6\% improvement over SAC on Ant-v4 and the best results on 4 out of 6 tasks.
Our ablation studies reveal that both \textbf{spherical normalization} and \textbf{adaptive concentration control} are essential to GAC's success.
These findings suggest that robust and efficient continuous control does not require complex distributions, but a principled respect for the geometry of action spaces. Code and pretrained models are available in supplementary materials.

TL;DR: We propose Geometric Action Control (GAC), a distribution-free policy architecture that generates actions directly on the unit sphere, eliminating tanh-squashing and entropy tuning while achieving higher returns with 50% fewer parameters.