# Discrete Action Space as a Prerequisite for GRPO Convergence in Small-Model Continuous Control

arXiv: https://arxiv.org/abs/2607.21626 · HTML: https://mlsanity.com/paper/2607.21626/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 15 of its 23 references that are in the map.
- First posted on arXiv 7 Jul 2026.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)

## Builds on (most cited first, 15 of 15)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [RT-2: Vision-Language-Action Models Transfer Web Knowledge to Robotic Control](https://mlsanity.com/paper/2307.15818/) (2023)
- [OpenVLA: An Open-Source Vision-Language-Action Model](https://mlsanity.com/paper/2406.09246/) (2024)
- [Learning to summarize from human feedback](https://mlsanity.com/paper/2009.01325/) (2020)
- [π0: A Vision-Language-Action Flow Model for General Robot Control](https://mlsanity.com/paper/2410.24164/) (2024)
- [Do As I Can, Not As I Say: Grounding Language in Robotic Affordances](https://mlsanity.com/paper/2204.01691/) (2022)
- [Asynchronous Methods for Deep Reinforcement Learning](https://mlsanity.com/paper/1602.01783/) (2016)
- [Code as Policies: Language Model Programs for Embodied Control](https://mlsanity.com/paper/2209.07753/) (2022)
- [Scaling Laws for Reward Model Overoptimization](https://mlsanity.com/paper/2210.10760/) (2022)
- [Inner Monologue: Embodied Reasoning through Planning with Language Models](https://mlsanity.com/paper/2207.05608/) (2022)
- [Eureka: Human-Level Reward Design via Coding Large Language Models](https://mlsanity.com/paper/2310.12931/) (2023)
- [Geometric Adaptive Control with Neural Networks for a Quadrotor UAV in Wind fields](https://mlsanity.com/paper/1903.02091/) (2019)

## Abstract (arXiv)

We study whether Group Relative Policy Optimization (GRPO) can fine-tune small language models for simulated quadrotor continuous-control tasks. In our benchmark, vanilla GRPO fine-tuning of Qwen-0.5B for 25 Hz quadrotor velocity control collapses to the trivial zero action: 0 percent success rate, with entropy falling from 0.35 to 0.03 within 60 steps. Two ablations - removing the jerk-penalty term and removing the KL anchor to the pretrained prior - each prevent entropy collapse, yet neither enables learning. When the action interface is replaced by a 5-way categorical choice over PID presets, training converges. The resulting controller traces a smoothness-reliability Pareto frontier along training duration; both endpoints are reported: 98.6 percent success with 0.656 m/s3 jerk at 64 steps, and 100 percent success with 1.103 m/s3 jerk, or 0.796 under a matched velocity cap, at 256 steps. The recipe is evaluated across three pretrained language models. As context, a re-tuned classical baseline, PID with Ki = 0.30 and vmax = 2.5, reaches the same 100 percent success rate at jerk 0.736 m/s3. A high-fidelity simulation using Crazyflie 2.1 dynamics surfaces a hover-region training-distribution gap.